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Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps

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  • Xie, Jiayi
  • Cui, Zhenyu
  • Zhang, Zhimin

Abstract

We propose for the first time some explicit closed-form Laguerre series expansion formulas for the first passage time density functions of a jump diffusion model. Suppose that the jumps in the model are phase-type distributed. In contrast to existing methods in the literature based on numerical Laplace transform inversion, the proposed formulas are in analytical closed-form and simple to implement. Two different methods are proposed to compute the Laguerre coefficients. Various numerical examples are also given to show the effectiveness of our method.

Suggested Citation

  • Xie, Jiayi & Cui, Zhenyu & Zhang, Zhimin, 2022. "Some new infinite series expansions for the first passage time densities in a jump diffusion model with phase-type jumps," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    • Handle: RePEc:eee:apmaco:v:429:y:2022:i:c:s0096300322003253
    DOI: 10.1016/j.amc.2022.127251
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    References listed on IDEAS

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    1. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    2. Lan Wu & Jiang Zhou & Shuang Yu, 2017. "Occupation Times of General Lévy Processes," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1565-1604, December.
    3. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
    4. Asmussen, Soren & Avram, Florin & Usabel, Miguel, 2002. "Erlangian Approximations for Finite-Horizon Ruin Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 267-281, November.
    5. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    6. Yasutaka Shimizu & Zhimin Zhang, 2019. "Asymptotically Normal Estimators of the Ruin Probability for Lévy Insurance Surplus from Discrete Samples," Risks, MDPI, vol. 7(2), pages 1-22, April.
    7. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    8. Yuzhen Wen & Chuancun Yin, 2014. "Exit Problems for Jump Processes Having Double-Sided Jumps with Rational Laplace Transforms," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, February.
    9. Dickson, David C.M. & Willmot, Gordon E., 2005. "The Density of the Time to Ruin in the Classical Poisson Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 45-60, May.
    10. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
    Full references (including those not matched with items on IDEAS)

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