Maximum principle for control problems with uncertain horizon and variable discount rate

We consider an optimal control problem in which the time horizon is a random variable and the discount factor may depend on the past state and control values. This problem combines features of controlled piecewise deterministic processes and recursive utility maximization. Applying a simple transformation and a refined version of Halkin's proof of the maximum principle for optimal control problems on unbounded time intervals (Ref. 1), we obtain the maximum principle for the problem under consideration. Our assumptions are weaker than those of related results in the literature.This research was supported by a grant from the Austrian Science Foundation, Vienna, Austria.