Optimal mean–variance reinsurance and investment in a jump-diffusion financial market with common shock dependence

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

Mathematical Methods of Operations Research, 2016, vol. 84, issue 1, No 7, 155-181

Abstract: Abstract In this paper, we study the optimal reinsurance-investment problems in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process, and the two jump number processes are correlated by a common shock. Moreover, we remove the assumption of nonnegativity on the expected value of the jump size in the stock market, which is more economic reasonable since the jump sizes are always negative in the real financial market. Under the criterion of mean–variance, based on the stochastic linear–quadratic control theory, we derive the explicit expressions of the optimal strategies and value function which is a viscosity solution of the corresponding Hamilton–Jacobi–Bellman equation. Furthermore, we extend the results in the linear–quadratic setting to the original mean–variance problem, and obtain the solutions of efficient strategy and efficient frontier explicitly. Some numerical examples are given to show the impact of model parameters on the efficient frontier.

Keywords: Mean–variance criterion; Hamilton–Jacobi–Bellman equation; Investment; Proportional reinsurance; Jump-diffusion process; Common shock; 91B28; 91B30; 93E20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s00186-016-0538-0

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