Randomized observation periods for the compound Poisson risk model: the discounted penalty function

Research output: Contribution to journalArticleResearchpeer-review

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 languageEnglish
Pages (from-to)424-452
Number of pages29
JournalScandinavian Actuarial Journal
Issue number6
DOIs
Publication statusPublished - 1 Nov 2013
Externally publishedYes

Fingerprint

Compound Poisson
Penalty Function
Risk Theory
Approximation Scheme
Continuous Time
Discrete-time
Limiting
Model
Numerical Examples
Observation
Risk model
Ruin
Penalty function

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.

In: Scandinavian Actuarial Journal, No. 6, 01.11.2013, p. 424-452.

Research output: Contribution to journalArticleResearchpeer-review

@article{afa0edd615d04f2dba81ad9ae367c8f3,
title = "Randomized observation periods for the compound Poisson risk model: the discounted penalty function",
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.",
keywords = "compound Poisson risk model, defective renewal equation, discounted density, Erlangization, Gerber-Shiu function",
author = "Hansj{\"o}rg Albrecher and Cheung, {Eric C.K.} and Stefan Thonhauser",
year = "2013",
month = "11",
day = "1",
doi = "10.1080/03461238.2011.624686",
language = "English",
pages = "424--452",
journal = "Scandinavian Actuarial Journal",
issn = "0346-1238",
publisher = "Taylor and Francis Ltd.",
number = "6",

}

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 -