Stationary distribution of the surplus process in a risk model with a continuous type investment
- Authors
- 조양현; 최승경; 이의용
- Issue Date
- Sep-2016
- Publisher
- 한국통계학회
- Keywords
- risk model; surplus process; stationary distribution; integro-differential equation; martingale; optional sampling theorem
- Citation
- Communications for Statistical Applications and Methods, v.23, no.5, pp 423 - 432
- Pages
- 10
- Journal Title
- Communications for Statistical Applications and Methods
- Volume
- 23
- Number
- 5
- Start Page
- 423
- End Page
- 432
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/3284
- DOI
- 10.5351/CSAM.2016.23.5.423
- ISSN
- 2287-7843
- Abstract
- In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.
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