Robust optimal excess-of-loss reinsurance and investment problem with p thinning dependent risks under CEV model

This paper is devoted to study a robust optimal excess-of-loss reinsurance and investment problem with p-thinning dependent risks for an ambiguity-averse insurer (AAI). Assume that the AAI's wealth process consists of two p-thinning dependent classes of insurance business. The AAI is allowed to purchase excess-of-loss reinsurance and invest in a financial market consisting of one risk-free asset and one risky asset, where risky asset's price follows CEV model. Under the criterion of maximizing the expected exponential utility of AAI's terminal wealth, the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy are derived by employing techniques of stochastic control theory. Moreover, we provide the verification theorem and present some numerical examples to analyze the impacts of parameters on our optimal control strategies.