Title: Study of undiscounted non-linear optimal multiple stopping problems on unbounded intervals

Authors: Faouzi Trabelsi

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, Tunis-Belvédère 1002, Tunisia; Higher Institute of Computer Sciences and Mathematics of Monastir, Monastir University, Avenue de la Korniche, B.P. 223, Monastir 5000, Tunisia

Abstract: In this paper we formulate and solve a class of undiscounted non-linear optimal multiple stopping problems, where the underlying price process follows a general linear regular diffusion on an unbounded and closed subinterval of the state space and where the payoff/reward function is bounded, continuous and superadditive. We use and adapt general theory of optimal stopping for diffusion and we illustrate the developed optimal exercise strategies by the example of valuation of perpetual American-style fixed strike discretely random monitoring Asian put options on any unbounded closed interval of the form [ε,∞), where ε > 0 is a given lower bound.

Keywords: nonlinear multiple stopping; optimal multiple stopping; regular linear diffusion; perpetual American-style options; fixed strike random monitoring options; Asian options; put options; excessive functions; unbounded intervals; payoff function; reward function; theory of optimal stopping; valuation; option contracts.

DOI: 10.1504/IJMOR.2013.052462

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.2, pp.225 - 254

Available online: 05 Mar 2013 *

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