jats:pConsider a branching diffusion process on jats:boldR</jats:bold>jats:sup1</jats:sup> starting at the origin. Take a high level jats:italicu</jats:italic> > 0 and count the number jats:italicR</jats:italic>(jats:italicu</jats:italic>, jats:italicn</jats:italic>) of branches reaching jats:italicu</jats:italic> by generation jats:italicn</jats:italic>. Let jats:italicF</jats:italic>jats:subjats:italick</jats:italic>,jats:italicn</jats:italic></jats:sub>(jats:italicu</jats:italic>) be the probability jats:boldP</jats:bold>(jats:italicR</jats:italic>(jats:italicu</jats:italic>, jats:italicn</jats:italic>) < jats:italick</jats:italic>), jats:italick</jats:italic> = 1, 2, …. We study the limit limjats:subjats:italicn</jats:italic>→jats:italic∞</jats:italic></jats:sub>jats:italicF</jats:italic>jats:subjats:italick</jats:italic>,jats:italicn</jats:italic></jats:sub>(jats:italicu</jats:italic>) = jats:italicF</jats:italic>jats:subjats:italick</jats:italic></jats:sub>(jats:italicu</jats:italic>). More precisely, a natural equation for the probabilities jats:italicF</jats:italic>jats:subjats:italick</jats:italic></jats:sub>(jats:italicu</jats:italic>) is introduced and the structure of the set of solutions is analysed. We interpret jats:italicF</jats:italic>jats:subjats:italick</jats:italic></jats:sub>(jats:italicu</jats:italic>) as a potential ruin probability in the situation of a multiple choice of a decision taken at vertices of a ‘logical tree’. It is shown that, unlike the standard risk theory, the above equation has a manifold of solutions. Also an analogue of Lundberg′s bound for branching diffusion is derived.</jats:p>