A risk model with paying dividends and random environment

Bara Kim; Hwa Sung Kim; Jeongsim Kim

doi:10.1016/j.insmatheco.2007.08.001

A risk model with paying dividends and random environment

Bara Kim, Hwa Sung Kim, Jeongsim Kim

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

10 Citations (Scopus)

Abstract

We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

Original language	English
Pages (from-to)	717-726
Number of pages	10
Journal	Insurance: Mathematics and Economics
Volume	42
Issue number	2
DOIs	https://doi.org/10.1016/j.insmatheco.2007.08.001
Publication status	Published - 2008 Apr

Bibliographical note

Funding Information:
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). This research was also funded by a research grant from Kwangwoon University in 2007.

Keywords

Deficit distribution
Dividend
Environment process
Phase-type distribution
QBD (quasi-birth-and-death) process
Ruin probability

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1016/j.insmatheco.2007.08.001

Cite this

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title = "A risk model with paying dividends and random environment",

abstract = "We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.",

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note = "Funding Information: This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). This research was also funded by a research grant from Kwangwoon University in 2007. ",

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AU - Kim, Bara

AU - Kim, Hwa Sung

AU - Kim, Jeongsim

N1 - Funding Information: This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). This research was also funded by a research grant from Kwangwoon University in 2007.

PY - 2008/4

Y1 - 2008/4

N2 - We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

AB - We consider a discrete time risk model where dividends are paid to insureds and the claim size has a discrete phase-type distribution, but the claim sizes vary according to an underlying Markov process called an environment process. In addition, the probability of paying the next dividend is affected by the current state of the underlying Markov process. We provide explicit expressions for the ruin probability and the deficit distribution at ruin by extracting a QBD (quasi-birth-and-death) structure in the model and then analyzing the QBD process. Numerical examples are also given.

KW - Deficit distribution

KW - Dividend

KW - Environment process

KW - Phase-type distribution

KW - QBD (quasi-birth-and-death) process

KW - Ruin probability

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U2 - 10.1016/j.insmatheco.2007.08.001

DO - 10.1016/j.insmatheco.2007.08.001

M3 - Article

AN - SCOPUS:40949156693

SN - 0167-6687

VL - 42

SP - 717

EP - 726

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 2

ER -

A risk model with paying dividends and random environment

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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