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Expected Power Utility Maximization of Insurers

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Listed:
  • Hiroaki Hata

    (Hitotsubashi University)

  • Kazuhiro Yasuda

    (Hosei university)

Abstract

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer who wishes to maximize the expected power utility of its terminal wealth on finite time horizon. We are also interested in the problem of maximizing the growth rate of expected power utility per unit time on the infinite time horizon. The risk process of the insurer is described by an approximation of the classical Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and multiple risky assets. The mean returns of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. With this setting, Hamilton–Jacobi–Bellman equations that are derived via a dynamic programming approach have explicit solution obtained by solving a matrix Riccati equation. Hence, the optimal investment and reinsurance strategies can be constructed explicitly. Finally, we present some numerical results related to properties of our optimal strategy and the ruin probability using the optimal strategy.

Suggested Citation

  • Hiroaki Hata & Kazuhiro Yasuda, 2024. "Expected Power Utility Maximization of Insurers," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(3), pages 543-577, September.
    • Handle: RePEc:kap:apfinm:v:31:y:2024:i:3:d:10.1007_s10690-023-09425-8
    DOI: 10.1007/s10690-023-09425-8
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Hamilton–Jacobi–Bellman equation; Power utility; Risk process; Stochastic control; Stochastic factor model;
    All these keywords.

    JEL classification:

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

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