Title: On undiscounted non-linear optimal multiple stopping

Authors: Faouzi Trabelsi; Mootassam Belleh Zoghlami

Addresses: Department of Mathematics, Laboratory of Mathematical and Numerical Modelling in Engineering Science, National Engineering School of Tunis, Tunis El Manar University, B.P. 37, 1002 Tunis-Belvédère, Tunisia; Higher Institute of Computer Sciences and Mathematics of Monastir, University of Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia ' Department of Mathematics, Laboratory of Mathematical and Numerical Modelling in Engineering Science, National Engineering School of Tunis, Tunis El Manar University, B.P. 37, 1002 Tunis-Belvédère, Tunisia

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.

DOI: 10.1504/IJOR.2012.047512

International Journal of Operational Research, 2012 Vol.14 No.4, pp.387 - 416

Available online: 25 Jun 2012 *

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