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On Optimal Stopping Problems for Matrix-Exponential Jump-Diffusion Processes

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  04 February 2016

Yuan-Chung Sheu  and
Ming-Yao Tsai
Yuan-Chung Sheu*
Affiliation:
National Chiao Tung University
Ming-Yao Tsai*
Affiliation:
National Chiao Tung University
*
∗ Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
∗ Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
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Abstract

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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.

Keywords

Optimal stopping problemAmerican call-type reward functionaveraging problemmatrix-exponential distributionjump-diffusion process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J75: Jump processes 60G51: Processes with independent increments; L'evy processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 531 - 548
Copyright
© Applied Probability Trust 

Footnotes

Partially supported by NSC grant NSC100-2115-M-009-006, CMMSC, and NCTS, Taiwan.

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