Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed.

Keywords

Deficit at ruin, Renewal equation, Time of ruin, Ruin probability, Surplus prior to ruin, Surplus process

Publication Date

8-2003

Source Publication Title

Insurance: Mathematics and Economics

Volume

33

Issue

1

Start Page

59

End Page

66

Publisher

Elsevier

Peer Reviewed

1

Copyright

Copyright © 2003 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/S0167-6687(03)00143-4

ISSN (print)

01676687

Included in

Mathematics Commons

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