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Transient and Stationary Analyses of the Surplus in a Risk Model

Authors
조언영최승경이의용
Issue Date
Nov-2013
Publisher
한국통계학회
Keywords
Risk model; surplus process; characteristic function; integro-differential equation; stationary distribution.
Citation
Communications for Statistical Applications and Methods, v.20, no.6, pp 475 - 480
Pages
6
Journal Title
Communications for Statistical Applications and Methods
Volume
20
Number
6
Start Page
475
End Page
480
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/11478
DOI
10.5351/CSAM.2013.20.6.475
ISSN
2287-7843
Abstract
The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).
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