Transient and Stationary Analyses of the Surplus in a Risk Model
- Authors
- 조언영; 최승경; 이의용
- 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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