Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

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.

Keywords

First exit time, Ruin time, Ruin probability, Risk reserve process, Embrechts–Schmidli model

Publication Date

12-2002

Source Publication Title

Statistics and Probability Letters

Volume

60

Issue

4

Start Page

417

End Page

424

Publisher

Elsevier

Peer Reviewed

1

Copyright

Copyright © 2002 Elsevier Science B.V. All rights reserved.

Funder

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).

DOI

10.1016/S0167-7152(02)00311-5

ISSN (print)

01677152

Included in

Mathematics Commons

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