Conditions for balance between survival and ruin

Abstract

Let $\xi_t$ be a classic risk process or a risk process with stochastic premiums. We establish conditions for balance between ruin and survival in the case of zero initial capital $u = 0$ (ruin probability $q_{+} = \psi(0) = 1/2$, survival probability $p_{+} = 1 — q_{+} = 1/2$) and determine premium estimates under these conditions.