Optimal mean–variance investment/reinsurance with common shock in a regime-switching market

Junna Bi, Zhibin Liang () and Kam Chuen Yuen
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Junna Bi: East China Normal University
Zhibin Liang: Nanjing Normal University
Kam Chuen Yuen: The University of Hong Kong

Mathematical Methods of Operations Research, 2019, vol. 90, issue 1, No 5, 109-135

Abstract: Abstract In this paper, we consider the problem of optimal investment-reinsurance with two dependent classes of insurance risks in a regime-switching financial market. In our model, the two claim-number processes are correlated through a common shock component, and the market mode is classified into a finite number of regimes. We also assume that the insurer can purchase proportional reinsurance and invest its surplus in a financial market, and that the values of the model parameters depend on the market mode. Using the techniques of stochastic linear-quadratic control, under the mean–variance criterion, we obtain analytic expressions for the optimal investment and reinsurance strategies, and derive closed-form expressions for the efficient strategies and the efficient frontiers which are based on the solutions to some systems of linear ordinary differential equations. Finally, we carry out a numerical study for illustration purpose.

Keywords: Common shock; Efficient frontier; Mean–variance criterion; Optimal investment-reinsurance strategy; Regime-switching; Stochastic control; 62P05; 91B30; 93E20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-018-00657-3

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