Optimal reinsurance and investment for an insurer with the jump diffusion risk model in A-C case

In this paper, we study the optimal reinsurance and investment problem for a class of jump-diffusion model, where the diffusion term represents the additional claims (i.e. A-C case). The insurer can purchase proportional reinsurance while allowing she/he to invest in a risk-free asset and a risky asset. The price process of the risky asset is driven by geometric Levy process with dividend payouts. Applying stochastic control theory, the corresponding Hamilton-Jacobi-Bellman equation is established and the optimal reinsurance-investment strategies to maximize the expected exponential utility of terminal wealth are also established. Finally, the optimal strategies are analysed by the numerical simulation.