En iyi durma problemlerinin gürbüz eniyilemesi

Selling or buying an asset, selecting a job with the highest wage, searching for and purchasing a low-price item, and finding a qualified person to hire are examples of an important class of decisions which are called the optimal stopping problems. In this thesis, we analyze the optimal stopping problem where the decision maker is risk-sensitive. To model the risk-sensitive behavior of the decision maker, we employ time-dependent utility functions. First, we assume that the utility functions are known and derive a dynamic programming recursion whose unique solution yields the optimal strategy. Then, we investigate the case where some of the input parameters including the parameters of the utility function are not known with certainty. We formulate the corresponding optimal stopping problem with unknown utilities or unknown probability distribution of the outcomes as sequential games and propose a robust dynamic programming recursion to find the optimal strategy. We show that the optimal strategy has a reservation level property. Finally, we propose a utility assessment method which is applicable when the prior distribution of the unknown parameter is known.