<PAGE>
                                                                    Exhibit 10.5

                             MANAGEMENT AGREEMENT



                                    BETWEEN

                         USA OFFSHORE MANAGEMENT, LTD.

                                      AND

                        AMERINST INSURANCE COMPANY, LTD.


     THIS AGREEMENT is made and entered into this 2nd day of December, 1999,
between USA OFFSHORE MANAGEMENT, LTD., a Bermuda corporation with its principal
office in Hamilton, Bermuda (hereinafter referred to as "MANAGER"), and AmerInst
Insurance Company, Ltd. (on behalf of itself and related companies, AmerInst
Mezco, Ltd, AmerInst Insurance Group, Ltd. and AmerInst Investment Company,
Ltd.), a Bermuda corporation with its principal office in Hamilton, Bermuda
(hereinafter referred to as "COMPANY").


                              W I T N E S S E T H

     WHEREAS, MANAGER is a company engaged in managing and administering
insurance companies pursuant to section 10 of the Bermuda Insurance Act of 1978;
and

     WHEREAS, COMPANY desires to employ MANAGER serve as its Principal
Representative and to perform management and administration services in
connection with the operation of COMPANY, which is a Bermuda corporation
established pursuant to the Bermuda Insurance Act of 1978, and MANAGER is
willing to perform such services subject to the terms and conditions hereinafter
set forth; and

     WHEREAS, MANAGER represents and COMPANY believes that MANAGER has the
facilities and personnel in Bermuda to render the necessary management services
to COMPANY.
<PAGE>

     NOW, THEREFORE, in consideration of the mutual agreements herein contained,
the sufficiency of which is hereby acknowledged, and in consideration of the
performance by each of the parties hereto of the terms and agreements hereof, it
is agreed that:

                                   ARTICLE I
                                   ---------

                           Appointment and Authority
                           -------------------------


     1.1  The COMPANY hereby appoints MANAGER as its Principal Representative
(for the purposes described in this AGREEMENT) and hereby authorizes and directs
MANAGER to provide COMPANY management services hereof; MANAGER accepts such
appointment and undertakes and agrees to provide COMPANY with the services and
assistance herein provided upon the terms and conditions and for the
compensation herein specified.

     1.2  COMPANY retains all authority to perform on its own behalf such
          actions as it deems necessary to carry out the business of insurance.

                                   ARTICLE II
                                   ----------

                               Service of Manager
                               ------------------


     2.1  COMPANY, upon consultation with MANAGER, shall establish broad
principles to be applied by MANAGER in the performance of its duties under this
AGREEMENT.

     2.2  MANAGER, in the performance of its duties, agrees to do and perform
all acts reasonably as part of such management as customarily understood in the
insurance and reinsurance industry.

     2.3  Without limiting the generality of the foregoing, MANAGER specifically
agrees to perform the following services:

               (a) Maintain a home office and principal place of business in
          Bermuda for COMPANY during the term of this AGREEMENT and, if desired,
          recommend a person(s) who is a resident of Bermuda to serve as a
          director and/or officer.

          (b) Establish and maintain an accounting system appropriate to
          COMPANY'S operations and provide all accounting services required for
          purposes of
<PAGE>

          management and compliance with all requirements of Bermuda regulatory
          authorities (exclusive of audit and reserve certification services).
          In addition, MANAGER will duly perform all the duties and discharge
          all the responsibilities required of it as the COMPANY's Principal
          Representative by the Insurance Act 1978 and its Related Regulations
          and use its best endeavors to ensure that the Company is at all times
          in compliance with all statutes (including subordinate legislation and
          governmental or ministerial orders and decrees) in force from time to
          time regulating the activities of, or otherwise applicable to,
          insurers carrying on business in or from Bermuda.

          (c) Prepare financial statements at specified intervals and in the
          form requested by COMPANY as detailed in the attached Recordkeeping
          Addendum.

          (d) Submit on a timely basis to regulatory authorities such reports
          and other information as may be required by law, including statutory
          quarterly and annual statements and all returns for premium and other
          taxes required by the Bermuda tax authorities.

          (e) Render periodic advice, at such intervals and with such frequency
          as COMPANY may reasonably specify, as to the amount of reserves and
          other funds available for investment from time to time by COMPANY.

          (f) Perform certain insurance functions on behalf of COMPANY as
          outlined in the attached Insurance Addendum.

          (g) Perform certain shareholder relations functions on behalf of
          COMPANY as outlined in the attached Shareholder Relations addendum.

          (h) Maintain records of any funds due COMPANY and pay accounts payable
          owed by COMPANY of which MANAGER could reasonably be expected to have
          knowledge and which are required by the management duties assumed
          under this AGREEMENT including fees and charges of accountants,
          actuaries, lawyers and consultants.  MANAGER shall use diligence in
          the collection of accounts but shall be responsible to COMPANY only
          for funds which have been collected.  MANAGER shall not bear
          responsibility to pursue the collection of accounts through the use of
          court or other legal processes.
<PAGE>

          Specifically, MANAGER shall collect, receive and deposit all funds,
          including money and checks for premium on insurance, endorse "for
          deposit only" all checks payable to COMPANY, deposit such funds within
          fifteen (15) days of receipt only in checking and bank accounts in
          banks that are members of the Federal Reserve System or a Bermuda bank
          designated by the Board of COMPANY and abide in the respective
          accounts by the minimum and maximum amounts established by the Board;
          Manager shall hold all funds received by it in connection with this
          AGREEMENT as a fiduciary of COMPANY and segregated from its other
          funds and assets in compliance with all applicable laws and shall
          under no circumstances make any personal use of such funds.  Interest
          or revenue produced from such deposits shall inure to the benefit of
          COMPANY.

          (i) Assist COMPANY'S auditors in the audit of COMPANY'S books and
          records.

     2.4  COMPANY agrees to comply promptly with any request for instructions or
information which MANAGER may make in order to efficiently perform the
management duties under this AGREEMENT.  MANAGER shall bear no liability for its
failure to act or for its reasonable independent actions in connection with
COMPANY'S business in the absence of a timely response to any such request.

                                  ARTICLE III
                                  -----------

                              Manager Compensation
                              --------------------


     3.1  COMPANY hereby agrees to pay MANAGER as full compensation for all
services performed under this AGREEMENT the amount set forth in the Management
Fee Addendum at the intervals so specified. This amount is based on the
activities contemplated and responsibilities designated at the time of the
signing of this AGREEMENT. Changes in the operation or requirements of COMPANY
which change the services required of the MANAGER will be subject to review as
warranted with appropriate adjustment of the management fee, as mutually agreed.

     3.2  Promptly upon demand, COMPANY agrees to reimburse MANAGER for expenses
incurred directly on behalf of COMPANY, which are outside the ordinary course of
<PAGE>

providing the management services detailed in Article II.  These include, but
are not limited to, travel costs, COMPANY stationery, filing fees, premium
taxes, long distance telephone expenses, express delivery expense and like
matters.


                                   ARTICLE IV
                                   ----------

                              Term and Termination
                              --------------------


     4.1  This AGREEMENT shall be for the period commencing on the incorporation
of COMPANY through December 31, 2000, and shall automatically be renewed
annually thereafter for successive one-year periods.  However, either party may
terminate this Agreement without cause at any time after the first year by
giving the other party written notice of intention to terminate this Agreement,
and such notice shall be given not more than ninety (90) days, but not less than
sixty (60) days prior to the effective date of termination.

     4.2  Notwithstanding anything to the contrary herein, either party hereto
may terminate this AGREEMENT if the other party fails to perform or observe, or
commits a breach of, any provision of this AGREEMENT or is in violation of the
laws and regulations of Bermuda, and fails to cure or remedy such failure,
breach or violation within thirty (30) days following the delivery to such party
of a written notice specifying the alleged failure, breach or violation; such
termination to be effective upon the expiration of such thirty (30) day period.

     4.3  MANAGER agrees to cooperate with and assist COMPANY in the termination
of this AGREEMENT in all reasonable respects with regard to any matters arising
or occurring during the period this AGREEMENT is in force. COMPANY agrees to
reimburse MANAGER for all costs incurred by MANAGER with respect to the
cooperation and assistance provided by MANAGER pursuant to this Section 4.3.

     4.4  All books of account, insurance policies, reinsurance agreements, bank
statements and checks, loss information, minutes, correspondence and other
documentation maintained and held by MANAGER on behalf of and relating to the
affairs of COMPANY shall remain the sole and exclusive property of COMPANY and
shall be delivered promptly to COMPANY or its agent designated in writing
following any termination of this AGREEMENT by either party.
<PAGE>

                                   ARTICLE V
                                   ---------

                  Manager Responsibility; Limitations Thereon
                  -------------------------------------------


     5.1  MANAGER will use its best efforts and judgment to the end that the
services covered by this AGREEMENT shall at all times be performed in accordance
with such methods and in such manner as will comply with all laws and statutes
relating thereto and with all provisions of pertinent contracts and agreements
to the extent that COMPANY specifically notifies MANAGER of such provisions.
MANAGER does not hereby represent that it can or will render legal advice to
COMPANY or (except as otherwise expressly provided herein) that it will bear the
responsibility for COMPANY'S compliance with applicable legal requirements.
Rather, MANAGER will make reasonable efforts to conform its services to such
legal and contractual requirements as are made known to it.

     5.2  MANAGER shall indemnify and hold harmless COMPANY from and against any
liability, claims and expenses resulting from conduct of MANAGER.  However,
liability of MANAGER for any loss, injury or damages sustained by COMPANY as a
result of any act or omission of MANAGER shall not exceed an amount equal to the
annual fee actually received by MANAGER under and by virtue of this AGREEMENT,
except in cases where such loss, injury or damages result from the willful
misconduct, gross negligence or fraud of MANAGER.

     5.3  COMPANY shall defend and indemnify MANAGER and hold it harmless from
and against any and all liability, costs and expenses (including attorneys'
fees) arising out of or in any way relating to its management of COMPANY, except
liability which is a direct result of MANAGER'S gross negligence, willful or
wanton misconduct or fraud.

     5.4  MANAGER does not act as an insurer for any insured of COMPANY.  This
AGREEMENT shall not be construed as an insurance policy or any contract or
agreement of indemnity; it being understood that MANAGER is in no event under
the terms of this AGREEMENT financially responsible or liable for the payment or
satisfaction of claims, lawsuits or any cause of action against COMPANY or any
insured of COMPANY. The payment by MANAGER of any funds for the satisfaction of
any claim, lawsuit, or cause of action against COMPANY or any insured of COMPANY
shall not be considered an undertaking by MANAGER to be responsible financially
or liable for any present or future claims.

     5.5  MANAGER shall have no authority to hold itself out as an agent of
COMPANY for any other purpose than specifically prescribed in this AGREEMENT; to
waive any forfeiture; or to collect any premium except those for which policies
have been issued or valid receipts which have been sent for collection, or to
bind COMPANY in any way except as herein expressly stated.
<PAGE>

     5.6  MANAGER agrees that no forms, binders, pamphlets, booklets or any
other printed matter using COMPANY'S name shall be used, issued or circulated
unless authorized by COMPANY'S Board.

     5.7  Other than as provided by this AGREEMENT, the MANAGER is forbidden to
incur any indebtedness on behalf of the COMPANY whatsoever without first
obtaining the written consent of the Board of Directors of the COMPANY.

                                   ARTICLE VI
                                   ----------

                                Confidentiality
                                ---------------


     6.1  MANAGER shall not (except in the exercise of duties hereunder or as
required by law) disclose an information relating to the affairs of COMPANY to
any person not authorized by COMPANY to receive such information and MANAGER
will use its best efforts to prevent any such disclosure by its employees and
agents.

     6.2  All books and records of COMPANY shall be open to inspection only by
directors, officers and employees of MANAGER and by COMPANY'S officers,
directors and designated employees, in person or by agent or attorney, upon
written demand, at any reasonable time or times.

                                  ARTICLE VII
                                  -----------

                                 Miscellaneous
                                 -------------


     7.1  The failure of either party at any time to require the other party's
performance of any provision hereof shall not be construed as a waiver of any
continuing or succeeding breach of such provision, a waiver or modification of
the provision itself, or a waiver or modification of any other right under this
AGREEMENT.

     7.2  This AGREEMENT is governed by the laws of Bermuda.

     7.3  MANAGER shall at all times act as an independent contractor of
COMPANY, and in no event shall employees of MANAGER be considered employees of
COMPANY.

     7.4  This AGREEMENT (with all its addenda) constitutes the entire agreement
between the parties hereto concerning the subject matter addressed herein, and
supersedes all previous agreements or undertakings, whether oral or written.
This AGREEMENT may only be
<PAGE>

amended or modified in writing.

     7.5  Neither this AGREEMENT nor any right created hereunder may be assigned
by either party without the express written consent of the other.

     7.6  This AGREEMENT is binding upon the parties hereto, their successors
and assigns.

     7.7  Headings herein are for convenience of reference only and are not
intended for use in the interpretation of this AGREEMENT.

     7.8  No management personnel or other employees of the COMPANY are to
perform management functions and receive any remuneration therefore, through
this or any other management or service contract, in addition to compensation by
way of salary received directly from the COMPANY for their services.
<PAGE>

     IN WITNESS WHEREOF, the parties have caused this AGREEMENT to be executed
by their duly authorized representatives the day and year first mentioned above.


WITNESS:                            USA OFFSHORE MANAGEMENT, LTD.



/s/ Richard Lowther             By: /s/ Andrew Sargeant
-----------------------            -------------------------------
                                    Its duly authorized agent



WITNESS:                            AMERINST INSURANCE
                                    COMPANY, LTD.


/s/ Richard Lowther             By: /s/ Ronald Katch
-----------------------            ------------------------------
                                    Its duly authorized agent
<PAGE>

                             ADDENDA TO AGREEMENT

                                    BETWEEN

                        AMERINST INSURANCE COMPANY, LTD.

                                      AND

                         USA OFFSHORE MANAGEMENT, LTD.



INSURANCE ADDENDUM
------------------

MANAGER will:
-------------

(1)  Maintain and update all reinsurance policies, endorsements, binders, cover
     notes, and other evidence of insurance or reinsurance.

(2)  Issue Certificates of Insurance and act as COMPANY's registered agent for
     services of process.

(3)  Cooperate with authorized COMPANY employees, consultants, actuaries,
     auditors, claims personnel and attorneys on a day-to-day basis to ensure
     the efficient operation of the COMPANY.  The MANAGER also agrees to extend
     full cooperation to all regulatory and COMPANY officials during any and all
     audits or examinations.

RECORDKEEPING ADDENDUM
----------------------

MANAGER will:
-------------

(1)  Provide all routine accounting services to establish and maintain books of
     account, including, but not limited to, accounting for reinsurance,
     maintenance of underwriting statistics, invoicing, disbursements, cash and
     investment records and a general ledger.

(2)  Maintain true, accurate and complete records and accounts of all
     transactions arising out of this AGREEMENT, including, but not limited to,
     claims and losses, and financial matters.  Said records and accounts shall
     be maintained at all times in such a manner and form as may be agreed to by
     the Board of Directors of the COMPANY and in accordance with generally
     accepted accounting and insurance practices.

(3)  Prepare a quarterly financial statement of income and expenses, a balance
     sheet, and other financial statements as may be required by Company's
     Board, for distribution to such persons as are designated in writing by the
     Board; such reports shall include:

     (a)  premiums received;

     (b)  losses paid:
<PAGE>

     (c) loss adjustment expenses paid; and

     (d)  loss reserves information.

(4)  Complete and file Statutory Financial Return and Statutory Financial
     Statements as required by Bermuda insurance regulators.

(5)  Liaise with service providers preparing Premium Tax and COMPANY Tax and
     other regulatory returns in accordance with state and federal laws, and
     cause such returns to be filed with the appropriate authorities.

(6)  Ensure compliance with the regulations pertaining to books and records and
     Bermuda home office.

(7)  Prepare and maintain minutes of all board and shareholder meetings.  Assist
     in the preparation of the agenda and materials for the meetings.  Have a
     representative attend all board meetings and Committee meetings where
     necessary.

(8)  Advise the Board on matters of interest.

SHAREHOLDER RELATIONS ADDENDUM
------------------------------

COMPANY will:

(1)  Follow standard procedures for monitoring and responding to shareholder
     inquireies and requests as set forth by and under the direction of the
     Shareholder Relations Committee;

(2)  Receive and respond to shareholder telephone calls received on the 1-800
     number;

(3)  Maintain telephone log, including name of caller and brief description of
     nature of call. (Copy of which is sent to Chairman of Shareholder Relations
     Committee at end of every month);

(4)  Review and respond to shareholder inquiries and request received via email;

(5)  Compile and prepare stock transfer cases for Committee approval;

(6)  Compile and prepare stock redemption cases for Board approval;

(7)  Advise Committee members of abnormal shareholder calls or mail on cases
     requiring further assistance;

(8)  Maintain Buy-Sell Trading System list and prepare mailings to participants
     on a quarterly basis or as requested by the Committee;

(9)  Prepare special mailings as requested by the Committee;

(10) Coordinate with Harris Bank Shareholder Services Division, Transfer Agent
     for AmerInst Insurance Group, Ltd., on shareholder relations matters
     including transfer and redemption of
<PAGE>

     stock, change of address, dividends, proxy mailings, shareholder listings
     and other items relevant to shareholder relations.

(11) Maintain shareholder relations records.

MANAGEMENT AGREEMENT ADDENDUM
-----------------------------

COMPANY will:

(1)  Compensate MANAGER at a rate of $22,500 for the period ended December 31,
     1999.

(1)  Compensate MANAGER at a rate of $140,000 per annum through December 31,
     2001.

(2)  Cause the above agreement to be paid in quarterly installments in advance
     at the beginning of each calendar quarter.

(3)  Reimburse MANAGER for reasonable out-of-pocket expenses incurred during the
     management of the COMPANY including:  courier and express mail service;
     long-distance telephone calls; travel and meeting expenses incurred at the
     request of the COMPANY; costs of COMPANY stationery; filing fees; and
     similar expenses.

COMPANY agrees that special projects will be invoiced separately at agreed upon
fees or rates.

IN WITNESS WHEREOF, the parties have duly executed this Addendum this 2nd day of
July, 2000.



                                         USA OFFSHORE MANAGEMENT, LTD.
WITNESS:


/s/ Richard Lowther                           /s/ Andrew Sargeant
--------------------------------              -------------------------------
                                              It's Duly Authorized Agent



                                              AMERINST INSURANCE
WITNESS:                                      COMPANY, LTD.


/s/ Richard Lowther                           /s/ Ronald Katch
--------------------------------              -------------------------------
                                              It's Duly Authorized Agent