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Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion

Author

Listed:
  • Caibin Zhang

    (School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, P. R. China)

  • Zhibin Liang

    (School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Jiangsu 210023, P. R. China)

  • Kam Chuen Yuen

    (#x2020;Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong)

Abstract

This paper studies an optimal dynamic proportional reinsurance in a risk model with two dependent classes of insurance business. Under the criterion of maximizing the mean–variance utility of the terminal wealth with state-dependent risk aversion, we formulate the time-inconsistent problem within a game theoretic framework. By the technique of stochastic control theory, explicit expressions of the optimal results are derived not only for diffusion risk model but also for compound Poisson risk model. Furthermore, the similar problem with constant risk aversion is studied as well. Finally, some numerical examples are presented to show the impact of model parameters on the optimal strategies for both compound Poisson and diffusion cases.

Suggested Citation

  • Caibin Zhang & Zhibin Liang & Kam Chuen Yuen, 2019. "Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-45, March.
    • Handle: RePEc:wsi:ijfexx:v:06:y:2019:i:01:n:s242478631950004x
    DOI: 10.1142/S242478631950004X
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