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Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

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  • Hiroaki Hata
  • Kazuhiro Yasuda

Abstract

In this paper, we consider the problem of optimal investment by an insurer. The wealth of the insurer is described by a Cramér–Lundberg process. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend linearly on economic factors that are formulated as the solutions of linear stochastic differential equations. Moreover, the insurer preferences are exponential. With this setting, a Hamilton–Jacobi–Bellman equation that is derived via a dynamic programming approach has an explicit solution found by solving the matrix Riccati equation. Hence, the optimal strategy can be constructed explicitly. Finally, we present some numerical results related to the value function and the ruin probability using the optimal strategy.

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  • Hiroaki Hata & Kazuhiro Yasuda, 2018. "Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(5), pages 357-378, May.
    • Handle: RePEc:taf:sactxx:v:2018:y:2018:i:5:p:357-378
    DOI: 10.1080/03461238.2017.1350876
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    Cited by:

    1. 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.

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