The time to ruin and the number of claims until ruin for phase-type claims

Esther Frostig; Susan M. Pitts; Konstadinos Politis

doi:10.1016/j.insmatheco.2012.02.013

The time to ruin and the number of claims until ruin for phase-type claims

Esther Frostig, Susan M. Pitts, Konstadinos Politis

Department of Statistics

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

Abstract

We consider a renewal risk model with phase-type claims, and obtain an explicit expression for the joint transform of the time to ruin and the number of claims until ruin, with a penalty function applied to the deficit at ruin. The approach is via the duality between a risk model with phase-type claims and a particular single server queueing model with phase-type customer interarrival times; see Frostig (2004). This result specializes to one for the probability generating function of the number of claims until ruin. We obtain explicit expressions for the distribution of the number of claims until ruin for exponentially distributed claims when the inter-claim times have an Erlang- n distribution.

Original language	English
Pages (from-to)	19-25
Number of pages	7
Journal	Insurance: Mathematics and Economics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1016/j.insmatheco.2012.02.013
State	Published - Jul 2012

Bibliographical note

Funding Information:
The research of Esther Frostig was supported by the Israel Science Foundation grant 606/09 .

Keywords

Deficit at ruin
Duality
Extended Negative Binomial distribution
Number of claims to ruin
Renewal risk model
Ruin time

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1016/j.insmatheco.2012.02.013

Cite this

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abstract = "We consider a renewal risk model with phase-type claims, and obtain an explicit expression for the joint transform of the time to ruin and the number of claims until ruin, with a penalty function applied to the deficit at ruin. The approach is via the duality between a risk model with phase-type claims and a particular single server queueing model with phase-type customer interarrival times; see Frostig (2004). This result specializes to one for the probability generating function of the number of claims until ruin. We obtain explicit expressions for the distribution of the number of claims until ruin for exponentially distributed claims when the inter-claim times have an Erlang- n distribution.",

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AB - We consider a renewal risk model with phase-type claims, and obtain an explicit expression for the joint transform of the time to ruin and the number of claims until ruin, with a penalty function applied to the deficit at ruin. The approach is via the duality between a risk model with phase-type claims and a particular single server queueing model with phase-type customer interarrival times; see Frostig (2004). This result specializes to one for the probability generating function of the number of claims until ruin. We obtain explicit expressions for the distribution of the number of claims until ruin for exponentially distributed claims when the inter-claim times have an Erlang- n distribution.

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KW - Extended Negative Binomial distribution

KW - Number of claims to ruin

KW - Renewal risk model

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The time to ruin and the number of claims until ruin for phase-type claims

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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