Authors: Noureddine Jilani Ben Naouara; Faouzi Trabelsi
Addresses: Laboratoire de Recherche 'Analyse, probabilités et fractals' (LR18ES17), Department of Mathematics, Faculté des Sciences de Monastir, Ecole Supérieure Privée d'Ingénierie et de Technologies (ESPRIT), Université de Monastir, Avenue de l'Environnement - Monastir - 5000, Tunisia ' Laboratoire de Recherche 'Analyse, probabilités et fractals' (LR18ES17), Department of Mathematics, Faculté des Sciences de Monastir, Institut Supérieur d'Informatique et de Mathématiques de Monastir, Université de Monastir, Avenue de la Korniche, B.P. 223, 5000 Monastir, Avenue de l'Environnement - Monastir - 5000, Tunisia
Abstract: In this paper, we introduce a new optimal multiple stopping times problem, where we assume each exercise right happens before the date of release of a catastrophic event modelled by a random variable and this catastrophe can be natural (e.g., earthquake, tsunami) or technological (e.g., nuclear event). Since a sudden catastrophe will have a direct influence on prices variation, especially those of underlying as well as option's prime, eventual catastrophic event will be modelled by the first time the underlying's price exceeds some large barrier. The originality of this paper comes from a mathematical model taking account of a nonlinear criteria of sum of the underlying stopped at stopping times of the holder's filtration information as well as a random number of exercise rights at sopping times involving prior to a catastrophic event. This will generalises the concept of swing contracts, where the exercise rights number is only deterministic and finite.
Keywords: optimal multiple stopping; stopping times; catastrophic event; dynamic programming; RCLL process; diffusion process; Markov process; Snell's envelope.
International Journal of Mathematical Modelling and Numerical Optimisation, 2020 Vol.10 No.2, pp.214 - 237
Received: 26 Sep 2018
Accepted: 02 Aug 2019
Published online: 13 Mar 2020 *