The Cramer–Lundberg model with stochastic premium process

In this paper the problem of ruin is considered for an insurance company. The premium process is a linear function of time in the classic Cramer–Lundberg model. The premium process is stochastic and it is also independent of a risk process. The nonruin probability is chosen as a measure of the payment ability. Integral equations and exponential bounds are obtained similarly with the classic Cramer–Lundberg model. That model with a discounting factor was also investigated in [L. S. Jilina, Prikladna Statistika, Aktuarna ta Finansova Matematika, 1 (2000), pp. 67–78 (in Russian)].