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Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk

Danping Li, Ximin Rong and Hui Zhao

Insurance: Mathematics and Economics, 2015, vol. 64, issue C, 28-44

Abstract: In this paper, we consider the time-consistent reinsurance–investment strategy under the mean–variance criterion for an insurer whose surplus process is described by a Brownian motion with drift. The insurer can transfer part of the risk to a reinsurer via proportional reinsurance or acquire new business. Moreover, stochastic interest rate and inflation risks are taken into account. To reduce the two kinds of risks, not only a risk-free asset and a risky asset, but also a zero-coupon bond and Treasury Inflation Protected Securities (TIPS) are available to invest in for the insurer. Applying stochastic control theory, we provide and prove a verification theorem and establish the corresponding extended Hamilton–Jacobi–Bellman (HJB) equation. By solving the extended HJB equation, we derive the time-consistent reinsurance–investment strategy as well as the corresponding value function for the mean–variance problem, explicitly. Furthermore, we formulate a precommitment mean–variance problem and obtain the corresponding time-inconsistent strategy to compare with the time-consistent strategy. Finally, numerical simulations are presented to illustrate the effects of model parameters on the time-consistent strategy.

Keywords: Reinsurance and investment; Mean–variance criterion; Time-consistent strategy; Stochastic interest rate; Stochastic inflation index; Stochastic control (search for similar items in EconPapers)
Date: 2015
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Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu

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