# Risk Theory with the Gamma Process

## Details

Serval ID

serval:BIB_3A1B400E4B49

Type

**Article**: article from journal or magazin.

Collection

Publications

Institution

Title

Risk Theory with the Gamma Process

Journal

ASTIN Bulletin

ISSN

0515-0361

1783-1350

1783-1350

Publication state

Published

Issued date

1991

Peer-reviewed

Oui

Volume

21

Number

02

Pages

177-192

Language

english

Abstract

Consider the classical compound Poisson model of risk theory, in which dividends are paid to the shareholders according to a barrier strategy. Let b* be the level of the barrier that maximizes the expectation of the discounted dividends until ruin. The aggregate claims process is modelled by a process with independent, stationary and nonnegative increments. Such a process is either compound Poisson or else a process with an infinite number of claims in each time interval, for example a gamma process. It is shown how classical risk theory, and in particular ruin theory, can be adapted to this model. A detailed analysis is given for the gamma process, for which tabulated values of the probability of ruin are provided.

Open Access

Yes

Create date

16/07/2018 15:45

Last modification date

21/08/2019 6:18