Optimal stopping for processes with independent increments , and applications

In this paper we present an explicit solution to the infinite-horizon optimal stopping problem for processes with stationary independent increments , where reward functions admit a certain representation in terms of the process at a random time. It is shown that it is optimal to stop at the first time the process crosses a level defined as the root of an equation obtained from the representation of the reward function. We obtain an explicit formula for the value function in terms of the infimum and supremum of the process , by making use of the Wiener-Hopf factorization. The main results are applied to several problems considered in the literature , to give a unified approach , and to new optimization problems from the finance industry. © Applied Probability Trust 2009