Optimal proportional reinsurance and investment problem with constraints on risk control in a general jump-diffusion financial market

Huiming Zhu, Ya Huang, Jieming Zhou, Xiangqun Yang, Chao Deng

Abstract


We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.


doi:10.1017/S1446181115000280

Keywords


jump-diffusion risk model; optimal investment strategy; proportional reinsurance; exponential utility; Hamilton–Jacobi–Bellman equation



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.8833



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.