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Stationary distribution of the surplus in a risk model with dividends and reinvestments

Authors
Kim, SunggonLee, Eui Yong
Issue Date
Dec-2015
Publisher
KOREAN STATISTICAL SOC
Keywords
Risk model; Stationary distribution; Surplus process; Level crossing argument; Impulse control
Citation
JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.44, no.4, pp 516 - 529
Pages
14
Journal Title
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
Volume
44
Number
4
Start Page
516
End Page
529
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/10150
DOI
10.1016/j.jkss.2015.01.005
ISSN
1226-3192
1876-4231
Abstract
A continuous time risk model with dividends and reinvestments is considered. We obtain an explicit formula of the stationary distribution of the surplus and the expected time to ruin after a reinvestment by adopting the level crossing argument. We also propose a scheme to approximate the stationary distribution of the surplus. As an example, we consider the case when the claims are exponentially distributed, Erlang distributed, and generalized hyperexponentially distributed. (C) 2015 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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