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On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models

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  • Gapeev, Pavel V.
  • Stoev, Yavor I.

Abstract

We compute the Laplace transforms of the first exit times for certain one-dimensional jump–diffusion processes from two-sided intervals. The method of proof is based on the solutions of the associated integro-differential boundary value problems for the corresponding value functions. We consider jump–diffusion processes solving stochastic differential equations driven by Brownian motions and several independent compound Poisson processes with multi-exponential jumps. The results are illustrated on the non-affine pure jump analogues of certain mean-reverting or diverting diffusion processes which represent closed-form solutions of the appropriate stochastic differential equations.

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  • Gapeev, Pavel V. & Stoev, Yavor I., 2017. "On the Laplace transforms of the first exit times in one-dimensional non-affine jump–diffusion models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 152-162.
    • Handle: RePEc:eee:stapro:v:121:y:2017:i:c:p:152-162
    DOI: 10.1016/j.spl.2016.10.011
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    Cited by:

    1. Pavel V. Gapeev & Oliver Brockhaus & Mathieu Dubois, 2018. "On Some Functionals Of The First Passage Times In Models With Switching Stochastic Volatility," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 1-21, February.

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