On undiscounted non-linear optimal multiple stopping

Faouzi Trabelsi and Mootassam Belleh Zoghlami

International Journal of Operational Research, 2012, vol. 14, issue 4, 387-416

Abstract: 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.

Keywords: undiscounted nonlinear optimal multiple stopping; vector-valued approach; Snell envelope; diffusion process; regular diffusion; Markovian process; perpetual American-style discretely monitored Asian options; excessive functions. (search for similar items in EconPapers)
Date: 2012
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