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A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms

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  • Djilali Ait-Aoudia

Abstract

This paper investigates the two‐sided first exit problem for a jump process having jumps with rational Laplace transform. The corresponding boundary value problem is solved to obtain an explicit formula for the first passage functional. Also, we derive the distribution of the first passage time to two‐sided barriers and the value at the first passage time.

Suggested Citation

  • Djilali Ait-Aoudia, 2016. "A Note on First Passage Functionals for Lévy Processes with Jumps of Rational Laplace Transforms," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:5914657
    DOI: 10.1155/2016/5914657
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    References listed on IDEAS

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    1. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    2. 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..
    3. Xing, Xiaoyu & Zhang, Wei & Jiang, Yiming, 2008. "On the time to ruin and the deficit at ruin in a risk model with double-sided jumps," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2692-2699, November.
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