Optimal reinsurance and investment problem with default risk and bounded memory

Abstract

This paper considers an insurer with constant absolute risk aversion (CARA) preference and explores a reinsurance-investment optimisation problem where the insurer income is related to the historical wealth performance. The insurer can purchase proportional reinsurance contracts to transfer the claim risk and allocate the remaining liquid wealth in a savings account, a defaultable corporate zero-coupon bond and a risky asset with constant elasticity of variance (CEV) stochastic volatility. The problem is modelled using a stochastic system with delay. Under certain conditions, the analytic optimal reinsurance-investment policy is derived, and the corresponding verification theorem is provided. Finally, a sensitivity analysis is conducted on the optimal reinsurance-investment policies over different memory parameters. The results show that longer memory leads to more prudent reinsurance and investment decisions for the insurer.

Keywords:

• Default Risk
• optimal reinsurance-investment strategy
• bounded memory
• CEV model
• Hamilton-Jacobi-Bellman equation

Acknowledgments

We would like to thank the anonymous referees for helpful comments which ultimately improved the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China (Grant Nos. 11801099, 11701106, 71871071, 71801057, 71703029, 71671062), the Ministry of Education of Humanities and Social Science project of China (Grant No. 18YJC910005), and by the Natural Science Foundation of Guangdong Province of China (Grant Nos. 2017A030310575, 2018B030311004), and Innovation Team Project of Guangdong Colleges and Universities of China (Grant No. 2016WCXTD012).