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

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• 作者：Pavel V. Gapeev^a ; ^{p.v.gapeev@lse.ac.uk} ; Yavor I. Stoev^b ; ^{ystoev@umich.edu}
• 关键词：primary ; 60J75 ; 60G40 ; 60E10 ; secondary ; 34B05 ; 60J60 ; 60G51
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：121
• 期：Complete
• 页码：152-162
• 全文大小：485 K
• 卷排序：121

文摘

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.