Equilibrium excess-of-loss reinsurance–investment strategy for a mean–variance insurer under stochastic volatility model

This article considers an optimal excess-of-loss reinsurance–investment problem for a mean–variance insurer, and aims to develop an equilibrium reinsurance–investment strategy. The surplus process is assumed to follow the classical Cramér–Lundberg model, and the insurer is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset. The market price of risk depends on a Markovian, affine-form and square-root stochastic factor process. Under the mean–variance criterion, equilibrium reinsurance–investment strategy and the corresponding equilibrium value function are derived by applying a game theoretic framework. Finally, numerical examples are presented to illustrate our results.