Abstract. The integral-differential equations for the survival probability, on finite and infinite time intervals, for the insurance company operating in the (B, S)-market are derived for the Cramer–Lundberg model with stochastic premiums. To derive the equations, smooth distribution densities of premiums and claims are not required. Refs: 9 titles.

Keywords: Samuelson model, non-ruin probability, stochastic premiums and claims, transition probability density, Ito equation.