Ruin probabilities of a bidimensional risk model with investment

We consider a classical risk model with the possibility of investment. We study two types of ruin in the bidimensional framework. Using the martingale technique, we obtain an upper bound for the infinite-time ruin probability with respect to the ruin time Tmax(u1,u2)Tmax(u1,u2). For each type of ruin, we derive an integral–differential equation for the survival probability, and an explicit asymptotic expression for the finite-time ruin probability.