Expected utility maximization of optimal stopping problems

We consider the problem of optimal stopping of an independent and identically distributed sequence of random variables with observation costs and no recall for a decision maker, who maximizes expected utility. Though this problem does not fit into the framework of dynamic programming, we derive a recursive algorithm to find the optimal solution. Moreover, we show that the optimal stopping strategy has the reservation level property for all utility functions and we investigate how attitude to risk affects the solution. In the case of exponential utility we derive an easy recursion for the reservation levels and determine the range of its possible values. The results are illustrated by several examples.