Optimal investment and reinsurance in a jump diffusion risk model

Xiang Lin, Peng Yang

Abstract


We consider an insurance company whose surplus is governed by a jump diffusion risk process. The insurance company can purchase proportional reinsurance for claims and invest its surplus in a risk-free asset and a risky asset whose return follows a jump diffusion process. Our main goal is to find an optimal investment and proportional reinsurance policy which maximizes the expected exponential utility of the terminal wealth. By solving the corresponding Hamilton–Jacobi–Bellman equation, closed-form solutions for the value function as well as the optimal investment and proportional reinsurance policy are obtained. We also discuss the effects of parameters on the optimal investment and proportional reinsurance policy by numerical calculations.

doi:10.1017/S144618111100068X

Keywords


jump diffusion risk model; proportional reinsurance; investment; compound Poisson process; exponential utility; Hamilton–Jacobi–Bellman equation



DOI: http://dx.doi.org/10.21914/anziamj.v52i0.2832



Remember, for most actions you have to record/upload into this online system
and then inform the editor/author via clicking on an email icon or Completion button.
ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.