The ruin problem for a Wiener process with state-dependent jumps-Reference-Cited by-同舟云学术

The ruin problem for a Wiener process with state-dependent jumps

Published:2020-05-01 Issue:1 Volume:16 Page:13-23
ISSN:1339-0015
Container-title:Journal of Applied Mathematics, Statistics and Informatics
language:en
Short-container-title:

Author:

Lefebvre M.¹

Affiliation:

1. Department of Mathematics and Industrial Engineering , Polytechnique Montréal, C.P. 6079, Succursale Centre-ville, Montréal, Québec , Canada H3C 3A7 .

Abstract

Abstract Let X(t) be a jump-diffusion process whose continuous part is a Wiener process, and let T (x) be the first time it leaves the interval (0,b), where x = X(0). The jumps are negative and their sizes depend on the value of X(t). Moreover there can be a jump from X(t) to 0. We transform the integro-differential equation satisfied by the probability p(x) := P[X(T (x)) = 0] into an ordinary differential equation and we solve this equation explicitly in particular cases. We are also interested in the moment-generating function of T (x).

Publisher

Walter de Gruyter GmbH

Subject

General Medicine

Link

https://www.sciendo.com/pdf/10.2478/jamsi-2020-0002

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