Time-consistent mean-variance reinsurance-investment in a jump-diffusion financial market

Abstract

This paper study an optimal time-consistent reinsurance-investment strategy selection problem in a financial market with jump-diffusion risky asset, where the insurance risk model is modulated by a compound Poisson process. The aggregate claim process and the price process of risky asset are correlated by a common Poisson process. The objective of the insurer is to choose an optimal time-consistent reinsurance-investment strategy so as to maximize the expected terminal surplus while minimizing the variance of the terminal surplus. Since this problem is time-inconsistent, we attack it by placing the problem within a game theoretic framework and looking for subgame perfect Nash equilibrium strategy. We investigate the problem using the extended Hamilton–Jacobi–Bellman dynamic programming approach. Closed-form solutions for the optimal reinsurance-investment strategy and the corresponding value functions are obtained. Numerical examples and economic significance analysis are also provided to illustrate how the optimal reinsurance-investment strategy changes when some model parameters vary.

Keywords:

• Time-consistency
• proportional reinsurance
• investment
• jump-diffusion process
• common shock

Acknowledgements

The author would like to thank the anonymous referees for their careful reading and helpful comments on an earlier version of this paper, which led to a considerable improvement of the presentation of the work.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This research is supported by the Scientific Research Foundation of Xijing University [grant number XJ160144]; Scientific Research Program Funded by Shaanxi Provincial Education Department [grant number 15JK2183]; National Natural Science Foundation of China [grant number 11271375]; Natural Science Basic Research Plan in Shaanxi Province of China [grant number 2016JM1024], [grant number 2016JM1032].