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A dynamic game approach for optimal consumption, investment and life insurance problem

Author

Listed:
  • Rosario Maggistro

    (University of Trieste)

  • Mario Marino

    (University of Trieste)

  • Antonio Martire

    (University La Sapienza Roma)

Abstract

In this paper, we consider a multi-agent portfolio optimization model with life insurance for two players with random lifetime under a dynamic game approach. Each player is a price-taker and invests in the market to maximize her own utility for consumption and bequest. The market is complete and consists of n different assets, of which $$n-1$$ n - 1 are risky with prices driven by Geometric Brownian motion, while one is risk-free. We analyze both the non-cooperative and cooperative scenarios, and by considering the family of CRRA utility functions, we determine the closed-form expressions of the optimal consumption, investment, and life insurance for both players. A sensitivity analysis is provided both to illustrate the impact of the biometric and risk aversion parameters on the optimal controls and to compare the non-cooperative strategies with the cooperative ones. As a result, we suggest that cooperation favors the consumption optimality, while non-cooperation promotes the coverage of the risk of death.

Suggested Citation

  • Rosario Maggistro & Mario Marino & Antonio Martire, 2025. "A dynamic game approach for optimal consumption, investment and life insurance problem," Annals of Operations Research, Springer, vol. 346(2), pages 1377-1398, March.
    • Handle: RePEc:spr:annopr:v:346:y:2025:i:2:d:10.1007_s10479-024-05847-3
    DOI: 10.1007/s10479-024-05847-3
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    More about this item

    Keywords

    Dynamic games; Non-cooperative vs cooperative games; Portfolio choice; Lifetime uncertainty; Life insurance;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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