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First exit from an open set for a matrix-exponential Lévy process

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  • Chen, Yu-Ting
  • Chen, Yu-Tzu
  • Sheu, Yuan-Chung

Abstract

We study the first exit from a general open set for a one-dimensional Lévy process, where the Lévy measure is proportional to a two-sided matrix-exponential distribution. Under appropriate conditions on the Lévy measure, we obtain an explicit solution for the joint distribution of the first-exit time and the position of the Lévy process upon first exit, in terms of the zeros and poles of the corresponding Laplace exponent. The present result complements several earlier works on the use of exit sets for Lévy processes with algebraically similar Laplace exponents, where exits from open intervals are the main focus.

Suggested Citation

  • Chen, Yu-Ting & Chen, Yu-Tzu & Sheu, Yuan-Chung, 2017. "First exit from an open set for a matrix-exponential Lévy process," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 104-110.
    • Handle: RePEc:eee:stapro:v:127:y:2017:i:c:p:104-110
    DOI: 10.1016/j.spl.2017.03.018
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    References listed on IDEAS

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    1. Yu-Ting Chen & Cheng Few Lee & Yuan-Chung Sheu, 2020. "An ODE Approach for the Expected Discounted Penalty at Ruin in a Jump-Diffusion Model," World Scientific Book Chapters, in: Cheng Few Lee & John C Lee (ed.), HANDBOOK OF FINANCIAL ECONOMETRICS, MATHEMATICS, STATISTICS, AND MACHINE LEARNING, chapter 41, pages 1561-1598, World Scientific Publishing Co. Pte. Ltd..
    2. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    3. Gerber, Hans U. & Landry, Bruno, 1998. "On the discounted penalty at ruin in a jump-diffusion and the perpetual put option," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 263-276, July.
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