Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion

Yongwu Li and Zhongfei Li

Insurance: Mathematics and Economics, 2013, vol. 53, issue 1, 86-97

Abstract: In this paper, we study an insurer’s optimal time-consistent strategies under the mean–variance criterion with state dependent risk aversion. It is assumed that the surplus process is approximated by a diffusion process. The insurer can purchase proportional reinsurance and invest in a financial market which consists of one risk-free asset and multiple risky assets whose price processes follow geometric Brownian motions. Under these, we consider two optimization problems, an investment–reinsurance problem and an investment-only problem. In particular, when the risk aversion depends dynamically on current wealth, the model is more realistic. Using the approach developed by Björk and Murgoci (2009), the optimal time-consistent strategies for the two problems are derived by means of corresponding extension of the Hamilton–Jacobi–Bellman equation. The optimal time-consistent strategies are dependent on current wealth, this case thus is more reasonable than the one with constant risk aversion.

Keywords: Time-consistency; Mean–variance; Proportional reinsurance; Equilibrium strategy; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (24)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:53:y:2013:i:1:p:86-97

DOI: 10.1016/j.insmatheco.2013.03.008

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