A potential-theoretic approach to optimal stopping in a spectrally Lévy Model
Masahiko Egami, Tomohiro Koike
Published: 2025/6/12
Abstract
We study a systematic solution method for optimal stopping problems of one-dimensional spectrally negative \lev processes. Our approach relies essentially on the potential theory, in particular the Riesz decomposition and the maximum principle. Using these mathematical results, we not only identify and prove the necessary and sufficient conditions of optimality for a broad class of reward functions, but also present a method to tackle general problems in a direct and constructive way (without pre-specifying the solution form). To reinforce the latter point, we provide a step-by-step solution procedure, which is applicable to complex solution structures including multiple double-sided continuation regions.