On undiscounted non-linear optimal multiple stopping (Q2627307)

Summary: We study and formulate an undiscounted non-linear optimal multiple stopping problem, with an application to the valuation of the perpetual American-style discretely monitored Asian options. When the reward process is continuous, we follow a vector-valued approach. Under the right-continuity of this process, the problem can be reduced to a sequence of ordinary optimal stopping problems. In the Markovian case, we characterise the value function of the problem in terms of excessive functions. Finally, in case of a regular diffusion, we provide an optimal sequence of stopping times. The results are illustrated by some examples, where the value function of the problem is given explicitly.