Stochastic differential reinsurance game with common-shock dependence under the discounted framework

This paper investigates a stochastic differential reinsurance game between two insurance companies under the discounted framework. One insurer aims to minimise the discounted goal-reaching probability that the difference between their surpluses falls below zero within a finite time, while the other seeks to maximise it. Meanwhile, we consider the dependent risk between two insurers through the common-shock dependence framework. Based on the best-response analysis, we obtain four candidate pure stationary Markov strategy structures. For each candidate, we solve the corresponding HJBI equation and verify the conditions under which it forms a Nash equilibrium. Finally, we provide some numerical examples and comprehensive analyses to illustrate the influence of some important parameters on the optimal results.