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Ben Latifa, Imène; Bonnans, Joseph Frédéric; Mnif, Mohamed

A general optimal multiple stopping problem with an application to swing options. (English) Zbl 1327.60098

Stochastic Anal. Appl. 33, No. 4, 715-739 (2015).
Summary: In their paper [Math. Finance 18, No. 2, 239–268 (2008; Zbl 1133.91499)], R. Carmona and N. Touzi studied an optimal multiple stopping time problem in a market where the price process is continuous. In this article, we generalize their results when the price process is allowed to jump. Also, we generalize the problem associated to the valuation of swing options to the context of jump diffusion processes. We relate our problem to a sequence of ordinary stopping time problems. We characterize the value function of each ordinary stopping time problem as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman variational inequality.

Cited in 5 Documents

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
60J60 Diffusion processes
60J75 Jump processes (MSC2010)
91G80 Financial applications of other theories
91B70 Stochastic models in economics
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49J40 Variational inequalities

Keywords:

optimal multiple stopping; swing options; jump diffusion processes; Snell envelope; Hamilton-Jacobi-Bellman variational inequality; viscosity solution

Citations:

Zbl 1133.91499
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Full Text: DOI HAL

References:

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