Abstract
We present a method to solve optimal stopping problems in infinite horizon for a Levy process when the reward function can be non-monotone. To solve the problem we introduce two new objects. Firstly, we define a random variable eta(x) which corresponds to the argmax of the reward function. Secondly, we propose a certain integral transform which can be built on any suitable random variable. It turns out that this integral transform constructed from eta(x) and applied to the reward function produces an easy and straightforward description of the optimal stopping rule. We illustrate our results with several examples. The method we propose allows to avoid complicated differential or integro-differential equations which arise if the standard methodology is used.
[PDF] Slides of the presentation.