<PAGE>   1


                                                                   EXHIBIT 10.5




             AGREEMENT WITH RESPECT TO PROJECT COMPLETION AGREEMENT

         AGREEMENT (the "Agreement"), dated as of June 3, 1999, among CLOSED
JOINT- STOCK COMPANY "FOREST-STARMA", a closed joint stock company, organized
and existing under the legislation of the Russian Federation (the "Company"),
THE PIONEER GROUP, INC., a corporation organized and existing under the laws of
the state of Delaware (the "U.S. Sponsor"), PIONEER FOREST, INC., a corporation
organized and existing under the laws of the state of Delaware and a wholly
owned subsidiary of the U.S. Sponsor (the "U.S. Sponsor Subsidiary"), and
OVERSEAS PRIVATE INVESTMENT CORPORATION, an agency of the United States of
America ("OPIC").


                                   WITNESSETH:

         WHEREAS, the Company, the U.S. Sponsor, International Joint Stock
Company "Starma Holding" (the "Russian Sponsor") and OPIC are parties to a
Project Completion Agreement dated as December 21, 1995 (the "Project Completion
Agreement");

         WHEREAS, all capitalized terms used herein and not otherwise defined
herein shall have their respective meanings set forth in the Finance Agreement
dated December 21, 1995, as amended to and including the date hereof, between
the Company and OPIC or in the Project Completion Agreement;

         WHEREAS, as a result of the Recapitalization, the U.S. Sponsor
Subsidiary will own 99%, and may own 100%, of the shares of capital stock of the
Company and the Russian Sponsor no longer holds any capital stock of the
Company; and


         NOW, THEREFORE, the parties agree as follows:

         1.   INDEMNITY.

              The U.S. Sponsor hereby indemnifies and holds harmless the
              Indemnified Persons from and against any and all losses,
              liabilities, obligations, damages, penalties, actions, judgments,
              suits, costs, expenses, or disbursements of any kind or nature
              whatsoever (Losses) that may be imposed on, incurred by, or
              asserted against any Indemnified Person in any way relating to the
              Contract of Pledge of Shares between the U.S. Sponsor Subsidiary
              and OPIC or the Recapitalization, if such Losses would not have
              occurred had the U.S. Sponsor and the Russian Sponsor not
              transferred their shares of the Company, directly or indirectly,
              to the U.S. Sponsor Subsidiary in connection with the
              Recapitalization. In particular, but without limitation, this
              indemnity extends to any Losses incurred by an Indemnified Person
              as a result of the bankruptcy


<PAGE>   2
                                       2




              of the U.S. Sponsor Subsidiary or due to the existence of any
              contract for pledge of shares in the Company which the U.S.
              Sponsor Subsidiary may have entered into, and having priority to,
              the contract for the Pledge of Shares with OPIC."

         2.   REPRESENTATIONS AND WARRANTIES.
              (a)   Each of the Company, the U.S. Sponsor, the U.S. Sponsor
                    Subsidiary represents and warrants to OPIC that this
                    Agreement constitutes a legal, valid and binding obligation
                    of it, enforceable against it in accordance with its terms.

              (b)   Each of the U.S. Sponsor and the U.S. Sponsor Subsidiary
                    represents and warrants to OPIC, jointly and severally that:
                    (i)    As of the effective date hereof the U.S. Sponsor
                           Subsidiary owns of record and beneficially, and the
                           U.S. Sponsor owns beneficially, 97%, and upon
                           completion of the Recapitalization will so own
                           beneficially at least 99%, of the issued and
                           outstanding shares of capital stock of the Company,
                           and the U.S. Sponsor owns of record and beneficially
                           all of the issued and outstanding shares of capital
                           stock of the U.S. Sponsor Subsidiary;

                    (ii)   As of the date hereof each of the representation and
                           warranties of the Sponsors in paragraphs (b) through
                           (j) of Section 8.A of the Project Completion
                           Agreement are true and accurate.

         3.   UNDERTAKING OF U.S. SPONSOR SUBSIDIARY. The U.S. Sponsor
              Subsidiary hereby agrees to be bound by, and jointly and severally
              responsible and liable for all obligations and liabilities of the
              U.S. Sponsor under, the terms of Project Completion Agreement and
              to appoint an agent for service of process satisfactory to OPIC in
              connection with this undertaking in compliance with the terms of
              Section 14(b) of the Project Completion Agreement and give written
              notice thereof to OPIC within 30 days after the date hereof.
              Notices to the U.S. Sponsor Subsidiary may be given to it at the
              following address:

                           60 State Street
                           Boston, MA 02109
                           Tel: 617-742-7825
                           Fax: 617-422-4286

         4.   RATIFICATION AND CONFIRMATION. All the terms and provisions of the
              Project Completion Agreement are hereby ratified and confirmed by
              the U.S. Sponsor and the U.S. Sponsor Subsidiary and shall apply
              in full force and effect.

         5.   EFFECTIVE DATE.  This Agreement shall be effective as of the date
              hereof.

         6.   COUNTERPARTS. This Agreement may be executed in counterparts, each
              of which when so executed and delivered shall be deemed an
              original and all of which shall constitute one and the same
              instrument.


<PAGE>   3
                                       3



         IN WITNESS whereof, the parties hereto have caused this Agreement to be
  executed by their authorized representatives as of the day and year first
  above written.




                          CLOSED JOINT-STOCK COMPANY "FOREST-STARMA"


                          By:  /s/ Donald H. Hunter
                          Its: Authorized Officer


                          By:  /s/ Catherine V. Mannick
                          Its: Authorized Officer


                          By:  /s/ Inna Verdini
                          Its: Chief Accountant


                          THE PIONEER GROUP, INC.


                          By:  /s/ Eric W. Reckard
                          Its: Executive Vice President, CFO and Treasurer


                          PIONEER  FOREST, INC.


                          By:  /s/ Stephen G. Kasnet
                          Its: President


                          OVERSEAS PRIVATE INVESTMENT CORPORATION


                          By:  /s/ Steven S. Smith
                          Its: Investment Officer