ABSTRACT
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.
Funding
This research was supported by the National Natural Science Foundation of China under Grant Nos. (11301376, 71573110).
Notes
1 As shown in Chen et al. (Citation2014) and Sun et al. (Citation2016), for a dynamic optimization problem, if the strategy is optimal for the decision-maker at some time t1, and for any later time t2 > t1, she will follow the strategy
because it is still optimal at time t2, i.e.,
for all t > t2, then it is called a time-consistent strategy. Under the game theory framework, the derived subgame perfect Nash equilibrium strategy is a time-consistent strategy, see, for example, Björk and Murgoci (Citation2010) and Björk et al. (Citation2014).