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                                                                       EXHIBIT A

                           AGREEMENT OF JOINT FILING

     In accordance with Rule 13d-1(f) under the Securities Exchange Act of
1934, as amended, the undersigned hereby agree to the joint filing on behalf of
each of them of a Statement on Schedule 13D, or any amendments thereto, with
respect to the Common Stock, no par value per share, of HSB Group, Inc. and that
this Agreement be included as an Exhibit to such filing.

     Each of the undersigned parties represents and warrants to the others that
the information contained in any amendment thereto about it will be true,
correct and complete in all material respects and in accordance with all
applicable laws. Each of the undersigned parties agrees to inform the others of
any changes in such information or of any additional information which would
require any amendment to the Schedule 13D and to promptly file such amendment.

     Each of the undersigned parties agrees to indemnify the others for any
losses, claims, liabilities or expenses (including reasonable legal fees and
expenses) resulting from, or arising in connection with, the breach by such
party of any of representations, warranties or agreements in this Agreement.

     This Agreement may be executed in any number of counterparts, each of
which shall be deemed to be an original and all of which together shall be
deemed to constitute one and the same Agreement.


     IN WITNESS WHEREOF, the undersigned hereby execute this Agreement as of
August 25, 2000.

                                            AMERICAN INTERNATIONAL GROUP, INC.


                                            By: /s/ Kathleen E. Shannon
                                               -----------------------------
                                               Name:  Kathleen E. Shannon
                                               Title: Vice President and
                                                      Secretary


                                            AMERICAN HOME ASSURANCE COMPANY

                                            By: /s/ Edward E. Matthews
                                               -----------------------------
                                               Name:  Edward E. Matthews
                                               Title: Senior Vice President


                                            THE INSURANCE COMPANY OF THE STATE
                                            OF PENNSYLVANIA

                                            By: /s/ Edward E. Matthews
                                               -----------------------------
                                               Name:  Edward E. Matthews
                                               Title: Senior Vice President


                                            COMMERCE AND INDUSTRY INSURANCE
                                            COMPANY

                                            By: /s/ Edward E. Matthews
                                               -----------------------------
                                               Name:  Edward E. Matthews
                                               Title: Senior Vice President


                                            AIG GLOBAL INVESTMENT CORP.

                                            By: /s/ Win J. Neuger
                                               -----------------------------
                                               Name:  Win J. Neuger
                                               Title: Chairman and Chief
                                                      Executive Officer