On stochastic non-linear discounting

We consider the problem of non-linear discounting in a stochastic formulation, and show that under some natural assumptions it reduces to a standard stochastic optimal control problem with minimizing total costs. The idea of such a reduction appeared in Piunovskiy, Presman, Zhang and Zheng (Annals of Operations Research, 2025, in press, doi.org/10.1007/s10479-025-06540-9). Here we present a more general formulation. Moreover, for the resulting stochastic optimal control problem, we, not only prove the existence of an optimal strategy, but also indicate the method for constructing it.