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

Pavel V. Gapeev and Yavor I. Stoev

Statistics & Probability Letters, 2017, vol. 121, issue C, 152-162

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.

Keywords: Jump–diffusion processes; First exit times; Laplace transforms; Solvable stochastic differential equations; Non-affine processes; Mean-reverting and diverting property (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2016.10.011

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