On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models

Mingsi Long and Hongzhong Zhang

Stochastic Processes and their Applications, 2019, vol. 129, issue 8, 2821-2849

Abstract: In the spirit of Surya (2007), we develop an average problem approach to prove the optimality of threshold type strategies for optimal stopping of Lévy models with a continuous additive functional (CAF) discounting. Under spectrally negative models, we specialize this in terms of conditions on the reward function and random discounting, where we present two examples of local time and occupation time discounting. We then apply this approach to recursive optimal stopping problems, and present simpler and neater proofs for a number of important results on qualitative properties of the optimal thresholds, which are only known under a few special cases Carmona and Touzi (2008), Leung et al. (2015) and Surya (2007).

Date: 2019
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DOI: 10.1016/j.spa.2018.08.005

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