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

Rosario Maggistro (), Mario Marino () and Antonio Martire ()
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Rosario Maggistro: University of Trieste
Mario Marino: University of Trieste
Antonio Martire: University La Sapienza Roma

Annals of Operations Research, 2025, vol. 346, issue 2, No 25, 1377-1398

Abstract: 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.

Keywords: Dynamic games; Non-cooperative vs cooperative games; Portfolio choice; Lifetime uncertainty; Life insurance (search for similar items in EconPapers)
JEL-codes: C61 C70 G11 G22 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-024-05847-3

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