Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset. Especially the price process of the risky asset is governed by Heston’s stochastic volatility(SV) model. With the objective of maximizing the expected index utility of the terminal wealth of the insurance company, by using the classical tools of stochastic optimal control, the explicit expressions for optimal strategies and optimal value functions are derived. An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper. Moreover, some numerical simulations and sensitivity analysis are provided.