Optimal excess-of-loss reinsurance and investment with stochastic factor process

Xiaoyu Kong and Yuhua Lü

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 24, 8705-8727

Abstract: In this paper, we study the problem of excess-of-loss reinsurance and investment for an insurer who wishes to maximize the expected exponential utility of the terminal wealth. The surplus process of the insurer is described by a Brownian motion with drift, while the claim arrival process, the insurance and reinsurance premiums are affected by a stochastic factor. It is also assumed that the risky asset in the financial market have time varying and random coefficients. By applying the Hamilton-Jacobi-Bellman (HJB) equation approach, both the value function and the corresponding optimal strategies are obtained and characterized under different premium calculation principles. Furthermore, the existence and uniqueness of the solution to the HJB equation is also discussed. Finally, numerical examples are presented to illustrate our results.

Date: 2022
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DOI: 10.1080/03610926.2021.1904989

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