Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a < b, we study the occupation time T-a,T-b(t), which is the total length of the time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of T-a,T-b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.

Keywords

Occupation time, Piecewise deterministic Markov process, Risk theory, Duration of negative surplus, Ruin

Publication Date

5-2002

Source Publication Title

Stochastic Models

Volume

18

Issue

2

Start Page

245

End Page

255

Publisher

INFORMS

Peer Reviewed

1

Copyright

Copyright © 2002 by Marcel Dekker, Inc.

DOI

10.1081/STM-120004466

Link to Publisher's Edition

http://dx.doi.org/10.1081/STM-120004466

ISSN (print)

15326349

ISSN (electronic)

15324214

Included in

Mathematics Commons

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