Risk minimization for an insurer with investment and reinsurance via g-expectation

Abstract

This paper is devoted to the study of a risk-based optimal investment and proportional reinsurance problem. The surplus process of the insurer and the risky asset process in the financial market are assumed to be general jump-diffusion processes. We use a convex risk measure generated by g-expectation to describe the risk of the terminal wealth with investment and reinsurance. Under the aim of minimizing the risk, the problem is solved by using techniques of stochastic maximum principles. Two interesting special cases are studied and the explicit expressions for optimal strategies and corresponding minimal risks are derived.

Keywords:

• Investment
• reinsurance
• g-expectation
• stochastic maximum principles
• Malliavin calculus

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 97M30
• 91G80
• 93E20
• 60H30

Disclosure statement

No potential conflict of interest was reported by the authors.

Acknowledgments

We are very grateful to the Editor and an anonymous referee for their insightful and detailed comments that improved the paper.

Additional information

Funding

Supported by the National Natural Science Foundation of China (Nos. 11701436 and 11661074), the Fundamental Research Funds for Central Universities (WHU: 2018IB019 and 2018IVB014) and the China Scholarship Council (No. 201706955015).