Robust optimal insurance and investment strategies for the government and the insurance company under mispricing phenomenon

This paper considers the robust optimal insurance-investment problem for the policyholder who is specified as a government and the insurance company with considering mispricing phenomenon. The government is allowed to purchase proportional insurance from the insurance company whose surplus process is assumed to follow the classical Cramér-Lundberg (C-L) model. Suppose the insurance company can invest in different financial markets and the government is limited to invest in one financial market. Thus, the insurance company is allowed to invest in a pair of mispriced stocks which offer statistical arbitrage opportunities, a risk-free asset, and a market index while the government is assumed to invest in a risk-free asset and a risky asset whose price process satisfies the geometric Brownian motion. Furthermore, we take the joint interest of the government and the insurance company into account. The government and the insurance company are both ambiguity-averse, aiming to maximize their expected joint product exponential utility of terminal wealth. By applying stochastic optimal control approach, we derive the robust equilibrium insurance-investment strategies and the corresponding equilibrium value function explicitly. In addition, we present some special cases of the model as extended results. Finally, numerical simulations are presented to illustrate the effects of model parameters on the optimal strategies.