On optimal stopping problems for matrix-exponential jump-diffusion processes

On optimal stopping problems for matrix-exponential jump-diffusion processes

Yuan-Chung Sheu and Ming-Yao Tsai

Source: J. Appl. Probab. Volume 49, Number 2 (2012), 531-548.

Abstract

In this paper we consider optimal stopping problems for a general class of reward functions under matrix-exponential jump-diffusion processes. Given an American call-type reward function in this class, following the averaging problem approach (see, for example, Alili and Kyprianou (2005), Kyprianou and Surya (2005), Novikov and Shiryaev (2007), and Surya (2007)), we give an explicit formula for solutions of the corresponding averaging problem. Based on this explicit formula, we obtain the optimal level and the value function for American call-type optimal stopping problems.

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Primary Subjects: 60G40, 60J75, 60G51

Keywords: Optimal stopping problem; American call-type reward function; averaging problem; matrix-exponential distribution; jump-diffusion process

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1339878803
Digital Object Identifier: doi:10.1239/jap/1339878803
Zentralblatt MATH identifier: 06053728
Mathematical Reviews number (MathSciNet): MR2977812

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