Article: New class of optimal multiple stopping times problems Journal: International Journal of Operational Research (IJOR) 2022 Vol.43 No.1/2 pp.226 - 253 Abstract: This paper is devoted to study a new discounted nonlinear optimal multiple stopping times problem with discounted factor β > 0 and infinite horizon. Under the right continuity of the underlying process, we show that the problem can be reduced to a sequence of ordinary optimal stopping problems. Next in the Markovian case, we characterise the value function of the problem in terms of β-excessive functions. Finally, in the special case of a diffusion process, we give explicit expressions for the value function of the problem as well as the optimal stopping strategy. As an explicit example in finance, we apply our theoretical results to manage a new generalised swing contract which gives its holder n rights to mark the price X of a stock, where the payment is only allowed at the final exercise time rather than at each exercise time as in the classical swing contact. Inderscience Publishers - linking academia, business and industry through research

Title: New class of optimal multiple stopping times problems

Authors: Noureddine Jilani Ben Naouara; Faouzi Trabelsi

Addresses: Department of Mathematics, Ecole Supérieure Privée d'Ingénierie et de Technologies (ESPRIT), Tunisia; Laboratoire de Recherche 'Analyse, Probabilités et Fractals' (LR18ES17), Faculté des Sciences de Monastir, Université de Monastir, Avenue de l'Environnement, Monastir – 5000, Tunisia ' Department of Mathematics, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Tunisia; Laboratoire de Recherche 'Analyse, Probabilités et Fractals' (LR18ES17), Faculté des Sciences de Monastir, Université de Monastir, Avenue de l'Environnement, Monastir – 5000, Tunisia

Abstract: This paper is devoted to study a new discounted nonlinear optimal multiple stopping times problem with discounted factor β > 0 and infinite horizon. Under the right continuity of the underlying process, we show that the problem can be reduced to a sequence of ordinary optimal stopping problems. Next in the Markovian case, we characterise the value function of the problem in terms of β-excessive functions. Finally, in the special case of a diffusion process, we give explicit expressions for the value function of the problem as well as the optimal stopping strategy. As an explicit example in finance, we apply our theoretical results to manage a new generalised swing contract which gives its holder n rights to mark the price X of a stock, where the payment is only allowed at the final exercise time rather than at each exercise time as in the classical swing contact.

Keywords: optimal multiple stopping; discounted factor; Markov process; diffusion process; Snell envelope; dynamic programming; β-excessive functions; swing option; COVID-19 pandemic.

DOI: 10.1504/IJOR.2022.121494

International Journal of Operational Research, 2022 Vol.43 No.1/2, pp.226 - 253

Received: 11 Nov 2019
Accepted: 24 Aug 2020
Published online: 16 Mar 2022 *

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Title: New class of optimal multiple stopping times problems

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