In this paper we study a stochastic differential game between two insurers whose surplus processes are modelled by quadratic-linear diffusion processes. We consider an exit probability game. One insurer controls its risk process to minimize the probability that the surplus difference reaches a low level (indicating a disadvantaged surplus position of the insurer) before reaching a high level, while the other insurer aims to maximize the probability. We solve the game by finding the value function and the Nash equilibrium strategy in explicit forms.
"A stochastic differential game for quadratic-linear diffusion processes." Adv. in Appl. Probab. 48 (4) 1161 - 1182, December 2016.