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A Potential-theoretic Approach to Optimal Stopping in a Spectrally Lévy Model

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  • Masahiko EGAMI
  • Tomohiro KOIKE

Abstract

We present a systematic solution method for optimal stopping problem of one-dimensional spectrally negative L´evy processes. Our main tools are based on the potential theory, particularly the Riesz decomposition and the maximum principle. This novel approach allows us to handle a broad class of reward functions. That is, we solve the problem in a general setup without relying on specific form of the reward function. We provide a step-by-step solution procedure, which is applicable to complex solution structures including multiple double-sided continuation regions.

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  • Masahiko EGAMI & Tomohiro KOIKE, 2025. "A Potential-theoretic Approach to Optimal Stopping in a Spectrally Lévy Model," Discussion papers e-25-007, Graduate School of Economics , Kyoto University.
    • Handle: RePEc:kue:epaper:e-25-007
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    References listed on IDEAS

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    3. Christensen, Sören & Crocce, Fabián & Mordecki, Ernesto & Salminen, Paavo, 2019. "On optimal stopping of multidimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2561-2581.
    4. A. Kyprianou & B. Surya, 2007. "Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels," Finance and Stochastics, Springer, vol. 11(1), pages 131-152, January.
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