The joint density function of three characteristics on jump-diffusion risk process

In this paper, we consider the jump-diffusion risk process, i.e., the classical risk process that is perturbed by diffusion. We derive the explicit expression for the joint density function of three characteristics: the time of ruin, the surplus immediately before ruin, and the deficit at ruin. By using the explicit joint density function, we extend some Dickson’s [Insurance: Mathematics and Economics 11 (1992) 191] results to the jump-diffusion risk process. We also obtain the distribution of the time that the negative surplus first reaches the level zero.