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Constrained investment–reinsurance optimization with regime switching under variance premium principle

Lv Chen, Linyi Qian, Yang Shen and Wei Wang

Insurance: Mathematics and Economics, 2016, vol. 71, issue C, 253-267

Abstract: This paper studies optimal investment and reinsurance problems for an insurer under regime-switching models. Two types of risk models are considered, the first being a Markov-modulated diffusion approximation risk model and the second being a Markov-modulated classical risk model. The insurer can invest in a risk-free bond and a risky asset, where the underlying models for investment assets are modulated by a continuous-time, finite-state, observable Markov chain. The insurer can also purchase proportional reinsurance to reduce the exposure to insurance risk. The variance principle is adopted to calculate the reinsurance premium, and Markov-modulated constraints on both investment and reinsurance strategies are considered. Explicit expressions for the optimal strategies and value functions are derived by solving the corresponding regime-switching Hamilton–Jacobi–Bellman equations. Numerical examples for optimal solutions in the Markov-modulated diffusion approximation model are provided to illustrate our results.

Keywords: Investment; Reinsurance; Regime switching; Variance premium principle; Hamilton–Jacobi–Bellman equation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:71:y:2016:i:c:p:253-267

DOI: 10.1016/j.insmatheco.2016.09.009

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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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