Ruin probability in the dual risk model with two revenue streams

Esther Frostig

doi:10.1016/j.orl.2018.01.002

Ruin probability in the dual risk model with two revenue streams

Esther Frostig

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The dual risk model describes the surplus of a company with fixed expense rate and occasional random income inflows, called gains. Consider the dual risk model with two streams of gains. Type I gains arrive according to a Poisson process, and type II gains arrive according to a general renewal process. We show that the survival probability of the company can be expressed in terms of the survival probability in a dual risk process with renewal arrivals with initial reserve 0, and the survival probability in the dual risk process with Poisson arrivals in finite time.

Original language	English
Pages (from-to)	211-214
Number of pages	4
Journal	Operations Research Letters
Volume	46
Issue number	2
DOIs	https://doi.org/10.1016/j.orl.2018.01.002
State	Published - Mar 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

Busy period
G/G/1
M/G/1
Random walk
Survival probability

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2018.01.002

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abstract = "The dual risk model describes the surplus of a company with fixed expense rate and occasional random income inflows, called gains. Consider the dual risk model with two streams of gains. Type I gains arrive according to a Poisson process, and type II gains arrive according to a general renewal process. We show that the survival probability of the company can be expressed in terms of the survival probability in a dual risk process with renewal arrivals with initial reserve 0, and the survival probability in the dual risk process with Poisson arrivals in finite time.",

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AB - The dual risk model describes the surplus of a company with fixed expense rate and occasional random income inflows, called gains. Consider the dual risk model with two streams of gains. Type I gains arrive according to a Poisson process, and type II gains arrive according to a general renewal process. We show that the survival probability of the company can be expressed in terms of the survival probability in a dual risk process with renewal arrivals with initial reserve 0, and the survival probability in the dual risk process with Poisson arrivals in finite time.

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KW - G/G/1

KW - M/G/1

KW - Random walk

KW - Survival probability

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Ruin probability in the dual risk model with two revenue streams

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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