Journal of Applied Probability

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

Yuan-Chung Sheu and Ming-Yao Tsai

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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.

Article information

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

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.jap/1339878803

Digital Object Identifier
doi:10.1239/jap/1339878803

Mathematical Reviews number (MathSciNet)
MR2977812

Zentralblatt MATH identifier
1252.60039

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J75: Jump processes 60G51: Processes with independent increments; Lévy processes

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

Citation

Sheu, Yuan-Chung; Tsai, Ming-Yao. On optimal stopping problems for matrix-exponential jump-diffusion processes. J. Appl. Probab. 49 (2012), no. 2, 531--548. doi:10.1239/jap/1339878803. https://projecteuclid.org/euclid.jap/1339878803


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References

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