### Abstract

In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.

Original language | English |
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Pages (from-to) | 424-452 |

Number of pages | 29 |

Journal | Scandinavian Actuarial Journal |

Issue number | 6 |

DOIs | |

Publication status | Published - 1 Nov 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

- compound Poisson risk model
- defective renewal equation
- discounted density
- Erlangization
- Gerber-Shiu function

### ASJC Scopus subject areas

- Statistics and Probability
- Economics and Econometrics
- Statistics, Probability and Uncertainty

### Fields of Expertise

- Information, Communication & Computing

### Cite this

**Randomized observation periods for the compound Poisson risk model : the discounted penalty function.** / Albrecher, Hansjörg; Cheung, Eric C.K.; Thonhauser, Stefan.

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

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TY - JOUR

T1 - Randomized observation periods for the compound Poisson risk model

T2 - the discounted penalty function

AU - Albrecher, Hansjörg

AU - Cheung, Eric C.K.

AU - Thonhauser, Stefan

PY - 2013/11/1

Y1 - 2013/11/1

N2 - In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.

AB - In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.

KW - compound Poisson risk model

KW - defective renewal equation

KW - discounted density

KW - Erlangization

KW - Gerber-Shiu function

UR - http://www.scopus.com/inward/record.url?scp=84885053212&partnerID=8YFLogxK

U2 - 10.1080/03461238.2011.624686

DO - 10.1080/03461238.2011.624686

M3 - Article

SP - 424

EP - 452

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

IS - 6

ER -