GABELLI CONVERTIBLE SECURITIES FUND INC /DE
DEF 14A, 1999-04-09
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<PAGE>   1
 
================================================================================
 
                                  SCHEDULE 14A
                                 (RULE 14A-101)
                    INFORMATION REQUIRED IN PROXY STATEMENT
                            SCHEDULE 14A INFORMATION
          PROXY STATEMENT PURSUANT TO SECTION 14(a) OF THE SECURITIES
                              EXCHANGE ACT OF 1934
                             (AMENDMENT NO.      )
 
Filed by the Registrant  [X]
 
Filed by a Party other than the Registrant  [ ]
 
Check the appropriate box:
 
<TABLE>
<S>                                            <C>
[ ]  Preliminary Proxy Statement               [ ]  CONFIDENTIAL, FOR USE OF THE COMMISSION
                                                    ONLY (AS PERMITTED BY RULE 14a-6(e)(2))
[X]  Definitive Proxy Statement
[ ]  Definitive Additional Materials
[ ]  Soliciting Material Pursuant to Rule 14a-11(c) or Rule 14a-12.
</TABLE>
 
                 The Gabelli Convertible Securities Fund, Inc.
                (NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)
 

    (NAME OF PERSON(S) FILING PROXY STATEMENT, IF OTHER THAN THE REGISTRANT)
 
Payment of Filing Fee (Check the appropriate box):
[X]  No fee required.
[ ]  Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.
 
     (1) Title of each class of securities to which transaction applies: .......
 
     (2) Aggregate number of securities to which transaction applies: ..........
 
     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (Set forth the amount on which the
         filing fee is calculated and state how it was determined): ............
 
     (4) Proposed maximum aggregate value of transaction: ......................
 
     (5) Total fee paid: .......................................................
 
[ ]  Fee paid previously with preliminary materials.
 
[ ]  Check box if any part of the fee is offset as provided by Exchange Act Rule
     0-11(a)(2) and identify the filing for which the offsetting fee was paid
     previously. Identify the previous filing by registration statement number,
     or the Form or Schedule and the date of its filing.
 
     (1) Amount Previously Paid: ...............................................
 
     (2) Form, Schedule or Registration Statement No.: .........................
 
     (3) Filing Party: .........................................................
 
     (4) Date Filed: ...........................................................
 
================================================================================
<PAGE>   2
 
                 THE GABELLI CONVERTIBLE SECURITIES FUND, INC.
                              One Corporate Center
                            Rye, New York 10580-1434
                                 (914) 921-5070
 
                            ------------------------
 
                    NOTICE OF ANNUAL MEETING OF SHAREHOLDERS
                           To Be Held on May 17, 1999
                            ------------------------
 
To the Shareholders of
THE GABELLI CONVERTIBLE SECURITIES FUND, INC.
 
     The Annual Meeting of Shareholders (the "Meeting") of The Gabelli
Convertible Securities Fund, Inc. (the "Fund") will be held at the Greenwich
Hyatt Regency, 1800 East Putnam Avenue, Greenwich, Connecticut 06870, on Monday,
May 17, 1999, at 8:30 a.m. During the Meeting, the Shareholders will vote on the
following proposals:
 
     1. To elect three (3) Directors of the Fund, two to be elected by the
        holders of the Fund's Common Stock and holders of its 8% Cumulative
        Preferred Stock ("Preferred Stock") voting together as a single class,
        and one to be elected by the holders of the Preferred Stock voting as a
        separate class (PROPOSAL 1);
 
     2. To ratify the selection of PricewaterhouseCoopers LLP as the independent
        accountants of the Fund for the year ending December 31, 1999 (PROPOSAL
        2); and
 
     3. To consider and vote upon such other matters as may properly come before
        the Meeting or any adjournment thereof.
 
     These items are discussed in greater detail in the attached Proxy
Statement.
 
     Shareholders of record at the close of business on March 17, 1999 are
entitled to be present and vote at the Meeting or any adjourned Meeting.
 
     YOUR VOTE IS IMPORTANT REGARDLESS OF THE SIZE OF YOUR HOLDINGS IN THE FUND.
WHETHER OR NOT YOU PLAN TO ATTEND THE MEETING, WE ASK THAT YOU PLEASE COMPLETE
AND SIGN THE ENCLOSED PROXY CARD AND RETURN IT PROMPTLY IN THE ENCLOSED ENVELOPE
WHICH NEEDS NO POSTAGE IF MAILED IN THE CONTINENTAL UNITED STATES. INSTRUCTIONS
FOR THE PROPER EXECUTION OF PROXIES ARE SET FORTH ON THE INSIDE COVER.
 
                                          By Order of the Directors
 
                                          JAMES E. MCKEE
                                          Secretary
 
April 6, 1999
<PAGE>   3
 
                      INSTRUCTIONS FOR SIGNING PROXY CARDS
 
     The following general rules for signing proxy cards may help you and avoid
the time and expense to the Fund involved in validating your vote if you do not
sign your proxy card properly.
 
     1. Individual Accounts: Sign your name exactly as it appears in the
        registration on the proxy card.
 
     2. Joint Accounts: Either party may sign, but the name of the party signing
        should conform exactly to the name shown in the registration.
 
     3. All Other Accounts: The capacity of the individuals signing the proxy
        card should be indicated unless it is reflected in the form of
        registration. For example:
 
<TABLE>
<CAPTION>
                        REGISTRATION                          VALID SIGNATURE
                        ------------                          ---------------
<S>                                                           <C>
CORPORATE ACCOUNTS
(1)  ABC Corp...............................................  ABC Corp.
(2)  ABC Corp...............................................  John Doe, Treasurer
(3)  ABC Corp.
          c/o John Doe, Treasurer...........................  John Doe
(4)  ABC Corp., Profit Sharing Plan.........................  John Doe, Trustee
TRUST ACCOUNTS
(1)  ABC Trust..............................................  Jane B. Doe, Trustee
(2)  Jane B. Doe, Trustee
          u/t/d 12/28/78....................................  Jane B. Doe
CORPORATE OR ESTATE ACCOUNTS
(1)  John B. Smith, Cust.
          f/b/o John B. Smith, Jr. UGMA.....................  John B. Smith
(2)  John B. Smith..........................................  John B. Smith, Jr., Executor
</TABLE>
<PAGE>   4
 
                 THE GABELLI CONVERTIBLE SECURITIES FUND, INC.
                            ------------------------
 
                         ANNUAL MEETING OF SHAREHOLDERS
                                  May 17, 1999
                            ------------------------
 
                                PROXY STATEMENT
 
     This Proxy Statement is furnished in connection with the solicitation of
proxies by the Directors of The Gabelli Convertible Securities Fund, Inc. (the
"Fund") for use at the Annual Meeting of Shareholders of the Fund to be held on
May 17, 1999, at 8:30 a.m., at the Greenwich Hyatt Regency, 1800 East Putnam
Avenue, Greenwich, Connecticut, and at any adjournments thereof (the "Meeting").
The Notice of Meeting, proxy card and Proxy Statement were mailed to
Shareholders on or about April 6, 1999.
 
     You may attend the Meeting and vote in person or you may complete and
return the attached proxy. Proxies that are properly signed, dated and received
before the Meeting will be voted as specified. If you specify a vote for any of
the Proposals 1 through 3, your proxy will be voted as you indicated. If you
simply sign and date the proxy but do not specify a vote of any of the Proposals
1 through 3, your shares will be voted in favor of each of the nominees for
Director and in favor of Proposal 2 and at the discretion of the proxies on any
matters arising under Proposal 3.
 
     On March 17, 1999, the record date for the Meeting, there were 7,921,545
shares of Common Stock and 1,200,000 shares of Preferred Stock outstanding.
Shareholders of record on March 17, 1999 are entitled to vote. Shares of both
the Common Stock and Preferred Stock are entitled to one vote on each proposal.
 
     The following persons were known to the Fund to be beneficial owners or
owners of record of 5% or more of its outstanding Shares of Common Stock and
Preferred Stock as of the record date:
 
<TABLE>
<CAPTION>
         NAME AND ADDRESS OF                                  AMOUNT OF SHARES
     BENEFICIAL/ RECORD OWNER(S)       TITLE OF CLASS      AND NATURE OF OWNERSHIP      PERCENT OF CLASS
     ---------------------------       --------------      -----------------------      ----------------
<S>                                    <C>             <C>         <C>                  <C>
Cede & Co FAST*                            Common      4,173,110   Shares (record)           52.68%
P.O. Box 20
Bowling Green Station
New York, NY 10274
Bear, Stearns Securities Corp.**           Common        785,150   Shares (record)            9.91%
One Metrotech Center North,
4th Floor
Brooklyn, NY 11201
Prudential Securities, Inc.**              Common        642,437   Shares (record)            8.12%
c/o ADP Proxy Services
51 Mercedes Way
Edgewood, NY 11717
</TABLE>
<PAGE>   5
 
<TABLE>
<CAPTION>
         NAME AND ADDRESS OF                                  AMOUNT OF SHARES
     BENEFICIAL/ RECORD OWNER(S)       TITLE OF CLASS      AND NATURE OF OWNERSHIP      PERCENT OF CLASS
     ---------------------------       --------------      -----------------------      ----------------
<S>                                    <C>             <C>         <C>                  <C>
Charles Schwab & Co., Inc.**               Common        576,423   Shares (record)            7.28%
c/o ADP Proxy Services
51 Mercedes Way
Edgewood, NY 11717
Mario J. Gabelli and affiliates***         Common      1,069,424   Shares (beneficial)       13.50%
One Corporate Center
Rye, NY 10580
Cede & Co FAST*                          Preferred     1,182,645   Shares (record)           98.55%
P.O. Box 20
Bowling Green Station
New York, NY 10274
Salomon Smith Barney, Inc.**             Preferred       545,286   Shares (record)           45.44%
333 W. 34th Street
New York, NY 10001
A.G. Edwards & Sons, Inc.**              Preferred        71,080   Shares (record)            5.92%
1 North Jefferson
St. Louis, MO 63103
</TABLE>
 
- ---------
 
  * A nominee partnership of The Depository Trust Company.
 
 ** Shares held at the Depository Trust Company.
 
*** Includes 126,846 shares owned directly by Mr. Gabelli, 680,011 shares owned
by Gabelli Funds, LLC or its affiliates, 46,408 shares owned by the Gabelli &
Company, Inc. Profit-Sharing Plan, and 216,159 shares owned by discretionary
accounts managed by GAMCO Investors, Inc., a wholly-owned subsidiary of Gabelli
Asset Management Inc.
 
                  SUMMARY OF VOTING RIGHTS ON PROXY PROPOSALS
 
<TABLE>
<CAPTION>
           PROPOSAL                        COMMON STOCKHOLDERS            PREFERRED STOCKHOLDERS
           --------                        -------------------            ----------------------
<S>                                   <C>                             <C>
1.  Election of Directors             Common and Preferred            Common and Preferred
                                      Stockholders, voting together   Stockholders, voting together
                                      as a single class, elect two    as a single class, elect two
                                      Directors: Anthonie C. van      Directors: Anthonie C. van
                                      Ekris and Salvatore J. Zizza    Ekris and Salvatore J. Zizza
                                                                      Preferred Stockholders, voting
                                                                      as a separate class, elect one
                                                                      Director: Anthony J. Colavita
2.  Selection of Accountant           Common and Preferred Stockholders, voting together as a single
                                      class
3.  Other Business                    Common and Preferred Stockholders, voting together as a single
                                      class
</TABLE>
 
                                        2
<PAGE>   6
 
                PROPOSAL 1: TO ELECT THREE DIRECTORS OF THE FUND
 
     The Board of Directors is divided into three classes, and each year the
term of office of one class expires. Anthonie C. van Ekris, Salvatore J. Zizza
and Anthony J. Colavita have each been nominated by the Board of Directors for
three-year terms set to expire at the 2002 Annual Meeting of Shareholders. These
terms continue, however, until successors are duly qualified and elected. All of
the Nominees are current Directors of the Fund and all of the current Directors
except Dugald A. Fletcher are also directors or trustees of other investment
companies for which Gabelli Funds, LLC or its affiliates serve as investment
adviser (the "Gabelli Funds"). There are no family relationships among any of
the Directors, nominees or executive officers of the Fund.
 
     The holders of both the Common Stock and Preferred Stock, voting together
as a class, are entitled to elect two Directors: Anthonie C. van Ekris and
Salvatore J. Zizza. The holders of the Preferred Stock, voting as a separate
class, are entitled to elect one Director: Anthony J. Colavita. Felix J.
Christiana, elected at the May 11, 1998 Annual Meeting of Shareholders by the
holders of the Preferred Stock, continues to serve as a Director until the 2001
Annual Meeting of Shareholders. The holders of Preferred Stock would elect the
minimum number of additional Directors that would represent a majority of the
Directors in the event that dividends on Preferred Stock are in arrears for two
full years. No dividend arrearages exist at this time.
 
     Unless authority is withheld, the persons named in the proxy intend to vote
the proxy FOR the election of the nominees named below. Each nominee has
indicated that he will serve if elected, but if any nominee should be unable to
serve, the proxy will be voted for any other person determined by the persons
named in the proxy in accordance with their judgment. The business address of
each Director is One Corporate Center, Rye, NY 10580-1434.
 
<TABLE>
<CAPTION>
                                                                 NUMBER AND PERCENTAGE OF
                                                                SHARES BENEFICIALLY OWNED
                                                                  DIRECTLY OR INDIRECTLY
                                                                   ON MARCH 17, 1999**
     NAME, POSITION WITH THE FUND, BUSINESS EXPERIENCE        ------------------------------
              DURING PAST FIVE YEARS, AND AGE                  COMMON              PREFERRED
     -------------------------------------------------         ------              ---------
<S>                                                           <C>                  <C>
 
NOMINEES TO SERVE UNTIL 2002 ANNUAL MEETING OF SHAREHOLDERS
- -----------------------------------------------------------
ANTHONY J. COLAVITA                                              23,920***            800***
     Director of the Fund since 1989. President and Attorney
     at Law in the law firm of Anthony J. Colavita, P.C. and
     director or trustee of 12 other Gabelli funds. Mr.
     Colavita is 64 years old.
ANTHONIE C. VAN EKRIS                                             9,658***             -0-
     Director of the Fund since 1992. Managing Director of
     Balmac International, Ltd.; Director of Spinnaker
     Industries, Inc.; Director of Stahel Mardmeyer A.Z. and
     director or trustee of 9 other Gabelli funds. Mr. van
     Ekris is 65 years old.
*SALVATORE J. ZIZZA                                              18,965***             -0-
     Director of the Fund since 1991. Chairman of The
     Bethlehem Corp. (ASE); Board Member of Hollis Eden
     Pharmaceuticals (OTC); former Executive Vice President
     of FMG Group (OTC), a healthcare provider; former
     President and Chief Executive Officer of the Lehigh
     Group, Inc., an electrical supply wholesaler; formerly
     Chairman of the Executive Committee and Director of
     Binnings Building Products, Inc.; Adviser to The
     Gabelli Growth Fund and director or trustee of 3 other
     Gabelli funds. Mr. Zizza is 53 years old.
</TABLE>
 
                                        3
<PAGE>   7
 
     The following Directors of the Fund will continue to serve in such capacity
until their terms of office expire and their successors are elected and
qualified.
 
<TABLE>
<CAPTION>
                                                                 NUMBER AND PERCENTAGE OF
                                                                SHARES BENEFICIALLY OWNED
                                                                  DIRECTLY OR INDIRECTLY
                                                                   ON MARCH 17, 1999**
     NAME, POSITION WITH THE FUND, BUSINESS EXPERIENCE        ------------------------------
              DURING PAST FIVE YEARS, AND AGE                  COMMON              PREFERRED
     -------------------------------------------------         ------              ---------
<S>                                                           <C>                  <C>
 
DIRECTORS SERVING UNTIL 2000 ANNUAL MEETING OF SHAREHOLDERS
- -----------------------------------------------------------
*DUGALD A. FLETCHER                                               9,822***             -0-
     Director of the Fund since 1989. President, Fletcher &
     Company, Inc.; Director (since February 1991) and
     formerly Chairman and Chief Executive Officer of
     Binnings Building Products, Inc.; Adviser to The
     Gabelli Growth Fund. Mr. Fletcher is 70 years old.
ANTHONY R. PUSTORINO                                              4,145***             -0-
     Director of the Fund since 1989. Certified Public
     Accountant; Professor of Accounting, Pace University,
     since 1965 and director or trustee of 8 other Gabelli
     funds. Mr. Pustorino is 73 years old.
E. VAL CERUTTI                                                    2,696***             -0-
     Director of the Fund since 1989. Chief Executive
     Officer of Cerutti Consultants, Inc.; Former President
     and Chief Operating Officer of Stella D'oro Biscuit
     Company (through 1992); Adviser, Iona College School of
     Business; Director of Lynch Corporation and director of
     1 other Gabelli fund. Mr. Cerutti is 60 years old.
</TABLE>
 
                                        4
<PAGE>   8
 
<TABLE>
<CAPTION>
                                                                 NUMBER AND PERCENTAGE OF
                                                                SHARES BENEFICIALLY OWNED
                                                                  DIRECTLY OR INDIRECTLY
                                                                   ON MARCH 17, 1999**
     NAME, POSITION WITH THE FUND, BUSINESS EXPERIENCE        ------------------------------
              DURING PAST FIVE YEARS, AND AGE                  COMMON              PREFERRED
     -------------------------------------------------         ------              ---------
<S>                                                           <C>                  <C>
DIRECTORS SERVING UNTIL 2001 ANNUAL MEETING OF SHAREHOLDERS
- -----------------------------------------------------------
*MARIO J. GABELLI, CFA                                        1,069,424(13.50%)        -0-
     Chairman of the Board, President and Chief Investment
     Officer of the Fund since 1989; Chairman of the Board,
     Chief Executive Officer and Chief Investment Officer of
     Gabelli Asset Management Inc. and Gabelli Funds, Inc.;
     Chairman of the Board and Chief Executive Officer of
     Lynch Corporation, a diversified manufacturing and
     communications services company; Director of East/West
     Communications, Inc. and officer and/or director or
     trustee of 12 other Gabelli funds. Mr. Gabelli is 56
     years old.
FELIX J. CHRISTIANA                                              14,092***             -0-
     Director of the Fund since 1989; Retired; formerly
     Senior Vice President of Dollar Dry Dock Savings Bank
     and director or trustee of 8 other Gabelli funds. Mr.
     Christiana is 73 years old.
*KARL OTTO POHL                                                    -0 -                -0-
     Director of the Fund since 1992. Member of the
     Shareholder Committee of Sal Oppenheim Jr. & Cie,
     private investment bank; Board Member of TrizecHahn
     Corporation, real estate company, and Zurich Allied,
     insurance; Director of Gabelli Asset Management Inc.,
     former President of the Deutsche Bundesbank and
     Chairman of its Central Bank Council from 1980 through
     1991 and director or trustee of 14 other Gabelli funds.
     Mr. Pohl is 69 years old.
DIRECTORS AND OFFICERS AS A GROUP                             1,153,415(14.56%)       800***
</TABLE>
 
- ---------
 
  * "Interested person" of the Fund, as defined in the Investment Company Act of
1940, as amended (the "1940 Act"). Mr. Gabelli is an "interested person" of each
fund as a result of his employment as an officer of the Fund and the Adviser.
Mr. Gabelli is a registered representative of Gabelli & Company, Inc., an
affiliated broker-dealer. Mr. Pohl is a director of Gabelli Asset Management
Inc., the parent company of the Adviser. Mr. Fletcher and Mr. Zizza each may be
an "interested person" as a result of their past association within the last
three years with Binnings Building Products, Inc., an entity which was
controlled by GLI, Inc., an affiliate of the Adviser.
 
 ** For this purpose "beneficial ownership" is defined under Section 13(d) of
the Securities Exchange Act of 1934, as amended (the "Exchange Act"). The
information as to beneficial ownership is based upon information furnished to
the Fund by the Directors.
 
*** Less than 1%.
 
                                        5
<PAGE>   9
 
EXECUTIVE OFFICERS OF THE FUND
 
     Officers of the Fund are appointed by the Directors to serve at the
pleasure of the Board. Listed below is a brief description of the recent
business experience of each executive officer of the Fund not included in the
listing of Directors. The business address of each of these officers is One
Corporate Center, Rye, New York 10580-1434.
 
<TABLE>
<CAPTION>
        NAME, POSITION WITH THE FUND            PRINCIPAL OCCUPATION DURING LAST FIVE YEARS AND AGE
        ----------------------------            ---------------------------------------------------
<S>                                            <C>
BRUCE N. ALPERT                                Executive Vice President and Chief Operating Officer
Vice President and Treasurer                   of the Investment Adviser since June 1988; Director
since 1989                                     and President of Gabelli Advisers, Inc.; Officer of
                                               all other registered investment companies advised by
                                               the Investment Adviser; Vice President of The
                                               Treasurer's Fund, Inc.; Vice President of Gabelli
                                               Westwood Funds. Age 47
JAMES E. MCKEE                                 Vice President, General Counsel and Secretary of the
Secretary since 1995                           Investment Adviser since 1995; Vice President and
                                               General Counsel of GAMCO Investors, Inc. since 1993
                                               and of Gabelli Asset Management Inc. since 1999;
                                               Secretary of the registered investment companies
                                               advised by the Investment Adviser and its affiliates.
                                               Age 36
PETER W. LATARTARA                             Assistant Vice President of the Fund since May 1997
Vice President since 1998                      and officer of one other Gabelli fund; formerly
                                               Assistant Vice President of Gabelli & Company, Inc.
                                               since 1996. Prior to 1996, Mr. Latartara was with the
                                               government relations firm of Black, Manafort, Stone
                                               and Kelly in Washington, D.C. Age 31
</TABLE>
 
COMPENSATION OF OFFICERS AND DIRECTORS
 
     The Fund pays each Director not affiliated with the Adviser or its
affiliates a fee of $5,000 per year plus $750 per meeting attended in person,
together with the Director's actual out-of-pocket expenses relating to
attendance at meetings. The aggregate remuneration paid by the Fund to such
Directors during the fiscal year ended December 31, 1998, amounted to $63,250.
No officers or employees of the Fund received more than $60,000 in compensation
from the Fund. Officers of the Fund who are employed by the Adviser receive no
compensation from the Fund. The following table shows the compensation paid to
the Fund's non-affiliated Directors by the Fund and the other Gabelli Funds
during the year ended December 31, 1998. No pension or retirement benefits are
accrued as part of Fund expenses.
 
                                        6
<PAGE>   10
 
                               COMPENSATION TABLE
                      FISCAL YEAR ENDED DECEMBER 31, 1998
 
<TABLE>
<CAPTION>
                                                                             TOTAL COMPENSATION
                                                      AGGREGATE                FROM THE FUND
                                                    COMPENSATION              COMPLEX PAID TO
                                                      FROM THE                 DIRECTORS AND
NAME OF DIRECTOR                                        FUND                     OFFICERS*
- ----------------                                    ------------             ------------------
<S>                                                 <C>                      <C>
MARIO J. GABELLI                                       $    0                     $      0(13)
E. VAL CERUTTI                                         $8,000                     $ 10,000(2)
FELIX J. CHRISTINA                                     $8,000                     $ 88,500(9)
ANTHONY J. COLAVITA                                    $8,000                     $ 82,000(13)
DUGALD A. FLETCHER                                     $8,000                     $ 16,000(2)
KARL OTTO POHL                                         $7,250                     $102,466(15)
ANTHONY R. PUSTORINO                                   $8,000                     $100,500(9)
ANTHONIE C. VAN EKRIS                                  $8,000                     $ 57,500(10)
SALVATORE J. ZIZZA                                     $8,000                     $ 51,000(5)
</TABLE>
 
- ---------
 
* Represents the total compensation paid to such persons during the calendar
year ended December 31, 1998 by investment companies (including the Fund) from
which such person receives compensation that are considered part of the same
fund complex as the Fund because they have common or affiliated investment
advisers. The number in parenthesis represents the number of such investment
companies.
 
     During the year ended December 31, 1998, the Directors of the Fund met four
times. Each Director then in office attended at least 75% of the meetings of
Directors and of any Committee of which he is a member. Felix J. Christiana and
Anthony R. Pustorino serve on the Fund's Audit Committee and are not "interested
persons" of the Fund as defined in the 1940 Act. The Audit Committee is
responsible for recommending the selection of the Fund's independent accountants
and reviewing all audit as well as non-audit accounting services performed for
the Fund. During the fiscal year ended December 31, 1998, the Audit Committee
met twice.
 
REQUIRED VOTE
 
     Election of each Director of the Fund requires the affirmative vote of the
holders of a plurality of the applicable classes of shares of the Fund
represented at the Meeting if a quorum is present.
 
     THE BOARD OF DIRECTORS RECOMMENDS THAT YOU VOTE "FOR" THE ELECTION OF EACH
NOMINEE.
 
                                        7
<PAGE>   11
 
      PROPOSAL 2: TO RATIFY THE SELECTION OF PRICEWATERHOUSECOOPERS LLP AS
                THE INDEPENDENT ACCOUNTANTS OF THE FUND FOR THE
                         YEAR ENDING DECEMBER 31, 1999
 
     Upon recommendation by the Audit Committee, PricewaterhouseCoopers LLP,
1177 Avenue of the Americas, New York, New York, 10036, has been selected by the
vote of a majority of those Directors who are not "interested persons" of the
Fund to serve as independent accountants for the Fund's fiscal year ending
December 31, 1999. PricewaterhouseCoopers LLP has advised the Fund that it is
independent with respect to the Fund in accordance with the applicable
requirements of the American Institute of Certified Public Accountants and the
Securities and Exchange Commission (the "Commission").
 
     Representatives of PricewaterhouseCoopers LLP are expected to be present at
the Meeting to answer appropriate questions and will be given the opportunity to
make a statement if they so desire.
 
REQUIRED VOTE
 
     Ratification of the selection of PricewaterhouseCoopers LLP as independent
accountants requires the affirmative vote of a majority of the votes cast by
holders of shares of the Fund (Common and Preferred Stockholders voting together
as a single class) represented at the Meeting if a quorum is present.
 
     THE BOARD OF DIRECTORS, INCLUDING THE "NON-INTERESTED" DIRECTORS,
RECOMMENDS THAT YOU VOTE "FOR" THE PROPOSAL TO RATIFY THE SELECTION OF
PRICEWATERHOUSECOOPERS LLP AS THE INDEPENDENT ACCOUNTANTS OF THE FUND FOR THE
YEAR ENDING DECEMBER 31, 1999.
 
              PROPOSAL 3: OTHER MATTERS TO COME BEFORE THE MEETING
 
     The Directors do not intend to present any other business at the Meeting,
nor are they aware that any shareholder intends to do so. If, however, any other
matters are properly brought before the Meeting, the persons named in the
accompanying form of proxy will vote on such matters in accordance with their
judgment.
 
                             ADDITIONAL INFORMATION
 
THE INVESTMENT ADVISER AND ADMINISTRATOR
 
     Gabelli Funds, LLC is the Fund's Investment Adviser and Administrator. The
business address of Gabelli Funds, LLC is One Corporate Center, Rye, New York
10580-1434.
 
COMPLIANCE WITH THE SECURITIES EXCHANGE ACT OF 1934
 
     Section 16(a) of the Exchange Act requires the Fund's officers and
Directors, officers and directors of the Adviser, affiliated persons of the
Adviser, and persons who own more than ten percent of a registered class of the
Fund's securities, to file reports of ownership and changes in ownership with
the Commission and the New York Stock Exchange. Officers, Directors and greater
than ten percent shareholders are required by Commission regulation to furnish
the Fund with copies of all Section 16(a) forms they file.
 
                                        8
<PAGE>   12
 
     Based solely on its review of the copies of such forms received by it, the
Fund believes that during 1998 such persons complied with all applicable filing
requirements under the Exchange Act.
 
QUORUM
 
     On matters upon which the Common and Preferred Stockholders vote together
as a single class, a majority of the shares entitled to vote, present in person
or represented by proxy, constitutes a quorum at the Meeting. On matters upon
which the Preferred Stockholders vote as a separate class, a majority of the
shares of Preferred Stock entitled to vote, present in person or represented by
proxy, constitutes a quorum at the Meeting.
 
     If a quorum is present at the Meeting but sufficient votes to approve any
of the proposed items are not received, the persons named as proxies may propose
one or more adjournments of the Meeting to permit further solicitation of
proxies. A shareholder vote may be taken on one or more of the proposals in this
Proxy Statement prior to the adjournment if sufficient votes have been received
and it is otherwise appropriate. Any such adjournment will require the
affirmative vote of a majority of those shares present at the Meeting in person
or by proxy. If a quorum is present, the persons named as proxies will vote
those proxies which they are entitled to vote FOR any such proposal in favor of
such an adjournment and will vote those proxies required to be voted for
rejection of any such item against any such adjournment.
 
ABSTENTIONS AND VOTING BY BROKERS
 
     The shares over which brokers have discretionary voting power, the shares
that represent "broker non-votes" (i.e., shares held by brokers or nominees as
to which (i) instructions have not been received from the beneficial owners or
persons entitled to vote and (ii) the broker or nominee does not have
discretionary voting power on a particular matter and accordingly does not vote
such shares), and the shares whose proxies reflect an abstention on any item are
all counted as shares present and entitled to vote for purposes of determining
whether the required quorum of shares exists. Under Maryland law, abstentions do
not constitute a vote "for" or "against" a matter and will be disregarded in
determining the "votes cast" on an issue. Proposal 1, the election of two
Directors by holders of both the Common Stock and the Preferred Stock voting as
a single class, requires the affirmative vote of the holders of a plurality of
the Fund's common and preferred shares present and voting at the Meeting, and
the election of one Director by holders of the Preferred Stock voting as a
separate class requires the affirmative vote of the holders of a plurality of
the shares of Preferred Stock present and voting at the Meeting. Proposal 2,
ratification of the selection of the independent accountants, requires the
affirmative vote of a majority of the Fund's shares present and voting at the
Meeting. Abstentions and broker non-votes do not constitute a vote "for" or
"against" a matter and will be disregarded in determining the "votes cast" on an
issue.
 
REVOCATION OF PROXIES
 
     You may revoke your proxy at any time before it is voted by delivering a
written notice of new revocation to the Secretary of the Fund, delivering a
later-dated proxy that is received by the Fund at or prior to the Meeting, or by
attending the Meeting and voting in person.
 
SOLICITATION OF PROXIES
 
     In addition to the solicitation of proxies by mail, officers of the Fund
and officers and regular employees of Gabelli Funds, LLC, the Fund's investment
adviser (the "Adviser"), and Boston EquiServe, the Fund's transfer
 
                                        9
<PAGE>   13
 
agent (the "Transfer Agent"), affiliates of the Adviser and Transfer Agent and
other representatives of the Fund also may solicit proxies by telephone,
telegraph or in person. In addition, the Fund has retained Georgeson and
Company, Inc. to assist in the solicitation of proxies for a fee estimated at
$3,000 plus reimbursement of expenses. The costs of solicitation and the
expenses incurred in connection with preparing the Proxy Statement and its
enclosures will be paid by the Fund. The Fund will reimburse brokerage firms and
others for their expenses in forwarding solicitation materials to the beneficial
owners of shares. The Fund's most recent annual report is available upon
request, without charge, by writing the Fund at One Corporate Center, Rye, New
York, 10580-1434 or calling the Fund at (800) 422-3554.
 
     Shareholders of the Fund will be informed of the voting results of the
Meeting in the Fund's Semi-Annual Report dated June 30, 1999.
 
                             SHAREHOLDER PROPOSALS
 
     All proposals by shareholders of the Fund which are intended to be
presented at the Fund's next Annual Meeting of Shareholders to be held in 2000,
must be received by the Fund for consideration for inclusion in the Fund's proxy
statement and proxy relating to that meeting not later than December 1, 1999.
 
     IT IS IMPORTANT THAT PROXIES BE RETURNED PROMPTLY. SHAREHOLDERS WHO DO NOT
EXPECT TO ATTEND THE MEETING ARE THEREFORE URGED TO COMPLETE, SIGN, DATE AND
RETURN THE PROXY CARD AS SOON AS POSSIBLE IN THE ENCLOSED POSTAGE PAID ENVELOPE.
 
                                                                     GBFCS-PS-99
                                       10
<PAGE>   14
[X] PLEASE MARK VOTES                                                         __
    AS IN THIS EXAMPLE                                                         |

<TABLE>
<S>                                                   <C>
=============================================         1. To elect two (2) Directors of the Fund:          FOR ALL    WITH-   FOR ALL
THE GABELLI CONVERTIBLE SECURITIES FUND, INC.                         ANTHONIE C. VAN EKRIS               NOMINEES   HELD    EXCEPT
=============================================                           SALVATORE J. ZIZZA                  [ ]       [ ]      [ ]
             COMMON SHAREHOLDER
                                                         NOTE: If you do not wish your shares voted "For" a particular nominee,
Mark box at right if an address change or comment [ ]          mark the "For All Except" box and strike a line through the nominee's
has been noted on the reverse side of this card.               name. Your shares will be voted "For" the remaining nominee.

CONTROL NUMBER:                                       2. To ratify the selection of PricewaterhouseCoopers  FOR    AGAINST   ABSTAIN
                                                         LLP as the independent accountants of the Fund
                                                         for the year ending December 31, 1999.             [ ]      [ ]       [ ]

                                                      3. In their discretion, the proxies are authorized to consider and vote upon
                                                         such other matters as may properly come before said Meeting or any 
                                                         adjournment thereof.
Please be sure to sign            --------------------
and date this Proxy               Date
- ------------------------------------------------------

- ---Shareholder sign here---------Co-owner sign here---   RECORD DATE SHARES:
</TABLE>
<PAGE>   15
COMMON           THE GABELLI CONVERTIBLE SECURITIES FUND, INC.            COMMON

               THIS PROXY IS SOLICITED ON BEHALF OF THE DIRECTORS

The undersigned hereby appoints Mario J. Gabelli, Anthony R. Pustorino, Felix J.
Christiana, James E. McKee and Bruce N. Alpert, and each of them, attorneys and
proxies of the undersigned, with full powers of substitution and revocation, to
represent the undersigned and to vote on behalf of the undersigned all shares of
The Gabelli Convertible Securities Fund, Inc. (the "Fund") which the undersigned
is entitled to vote at the Annual Meeting of Shareholders of the Fund to be held
at the Greenwich Hyatt Regency, 1800 East Putnam Avenue, Greenwich, Connecticut
06870 on Monday, May 17, 1999 at 8:30 a.m., and at any adjournments thereof. The
undersigned hereby acknowledges receipt of the Notice of Meeting and Proxy
Statement and hereby instructs said attorneys and proxies to vote said shares as
indicated herein. In their discretion, the proxies are authorized to vote upon
such other business as may properly come before the Meeting.

A majority of the proxies present and acting at the Meeting in person or by
substitute (or, if only one shall be so present, then that one) shall have and
may exercise all of the power and authority of said proxies hereunder. The
undersigned hereby revokes any proxy previously given.

This proxy, if properly executed, will be voted in the manner directed by the
undersigned shareholder. If no direction is made, this proxy will be voted FOR
the election of the nominees as directors and FOR Proposal 2 and in the
discretion of the proxy holder as to any other matter that may properly come
before the Meeting. Please refer to the Proxy Statement for a discussion of the
Proposals.


- --------------------------------------------------------------------------------
PLEASE VOTE, DATE AND SIGN ON REVERSE AND RETURN PROMPTLY IN THE ENCLOSED
ENVELOPE.
- --------------------------------------------------------------------------------

- --------------------------------------------------------------------------------
Please sign this proxy exactly as your name(s) appear(s) on the books of the 
Fund. If joint owners, either may sign. Trustees and other fiduciaries should 
indicate the capacity in which they sign, and where more than one name appears, 
a majority must sign. If a corporation, this signature should be that of an 
authorized officer who should state his or her title.
- --------------------------------------------------------------------------------

HAS YOUR ADDRESS CHANGED?                   DO YOU HAVE ANY COMMENTS?

- ------------------------------------        ------------------------------------

- ------------------------------------        ------------------------------------

- ------------------------------------        ------------------------------------
<PAGE>   16
[X] PLEASE MARK VOTES                                                         __
    AS IN THIS EXAMPLE                                                         |

<TABLE>
<S>                                                   <C>
=============================================         1. To elect three (3) Directors of the Fund:        FOR ALL    WITH-   FOR ALL
THE GABELLI CONVERTIBLE SECURITIES FUND, INC.                          ANTHONY J. COLAVITA                NOMINEES   HELD    EXCEPT
=============================================                         ANTHONIE C. VAN EKRIS                 [ ]       [ ]      [ ]
           PREFERRED SHAREHOLDER                                        SALVATORE J. ZIZZA

                                                         NOTE: If you do not wish your shares voted "For" a particular nominee(s),
Mark box at right if an address change or comment [ ]          mark the "For All Except" box and strike a line through the name(s)
has been noted on the reverse side of this card.               of the nominee(s). Your shares will be voted "For" the remaining
                                                               nominee(s).
CONTROL NUMBER:
                                                      2. To ratify the selection of PricewaterhouseCoopers  FOR    AGAINST   ABSTAIN
                                                         LLP as the independent accountants of the Fund
                                                         for the year ending December 31, 1999.             [ ]      [ ]       [ ]

                                                      3. In their discretion, the proxies are authorized to consider and vote upon
                                                         such other matters as may properly come before said Meeting or any 
                                                         adjournment thereof.
Please be sure to sign            --------------------
and date this Proxy               Date
- ------------------------------------------------------

- ---Shareholder sign here---------Co-owner sign here---   RECORD DATE SHARES:
</TABLE>
<PAGE>   17
PREFERRED        THE GABELLI CONVERTIBLE SECURITIES FUND, INC.         PREFERRED

               THIS PROXY IS SOLICITED ON BEHALF OF THE DIRECTORS

The undersigned hereby appoints Mario J. Gabelli, Anthony R. Pustorino, Felix J.
Christiana, James E. McKee and Bruce N. Alpert, and each of them, attorneys and
proxies of the undersigned, with full powers of substitution and revocation, to
represent the undersigned and to vote on behalf of the undersigned all shares of
The Gabelli Convertible Securities Fund, Inc. (the "Fund") which the undersigned
is entitled to vote at the Annual Meeting of Shareholders of the Fund to be held
at the Greenwich Hyatt Regency, 1800 East Putnam Avenue, Greenwich, Connecticut
06870 on Monday, May 17, 1999 at 8:30 a.m., and at any adjournments thereof. The
undersigned hereby acknowledges receipt of the Notice of Meeting and Proxy
Statement and hereby instructs said attorneys and proxies to vote said shares as
indicated herein. In their discretion, the proxies are authorized to vote upon
such other business as may properly come before the Meeting.

A majority of the proxies present and acting at the Meeting in person or by
substitute (or, if only one shall be so present, then that one) shall have and
may exercise all of the power and authority of said proxies hereunder. The
undersigned hereby revokes any proxy previously given.

This proxy, if properly executed, will be voted in the manner directed by the
undersigned shareholder. If no direction is made, this proxy will be voted FOR
the election of the nominees as directors and FOR Proposal 2 and in the
discretion of the proxy holder as to any other matter that may properly come
before the Meeting. Please refer to the Proxy Statement for a discussion of the
Proposals.


- --------------------------------------------------------------------------------
PLEASE VOTE, DATE AND SIGN ON REVERSE AND RETURN PROMPTLY IN THE ENCLOSED
ENVELOPE.
- --------------------------------------------------------------------------------

- --------------------------------------------------------------------------------
Please sign this proxy exactly as your name(s) appear(s) on the books of the 
Fund. If joint owners, either may sign. Trustees and other fiduciaries should 
indicate the capacity in which they sign, and where more than one name appears, 
a majority must sign. If a corporation, this signature should be that of an 
authorized officer who should state his or her title.
- --------------------------------------------------------------------------------

HAS YOUR ADDRESS CHANGED?                   DO YOU HAVE ANY COMMENTS?

- ------------------------------------        ------------------------------------

- ------------------------------------        ------------------------------------

- ------------------------------------        ------------------------------------


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