Department of Mathematics
This paper investigates the first exit time and the ruin time of a risk reserve process with reserve-dependent income under the assumption that the claims arrive as a Poisson process. We show that the Laplace transform of the distribution of the first exit time from an interval satisfies an integro-differential equation. The exact solution for the classical model and for the Embrechts–Schmidli model are derived.
First exit time, Ruin time, Ruin probability, Risk reserve process, Embrechts–Schmidli model
Source Publication Title
Statistics and Probability Letters
Copyright © 2002 Elsevier Science B.V. All rights reserved.
Research supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKBU/2075/98P) and also by the National Natural Science Foundation of China (Project No. 19801020).
Link to Publisher's Edition
Chiu, S., & Yin, C. (2002). The first exit time and ruin time for a risk process with reserve-dependent income. Statistics and Probability Letters, 60 (4), 417-424. https://doi.org/10.1016/S0167-7152(02)00311-5