Communications for Statistical Applications and Methods

  • 제20권6호
  • /
  • Pages.475-480
  • /
  • 2013
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Transient and Stationary Analyses of the Surplus in a Risk Model

  • 투고 : 2013.09.06
  • 심사 : 2013.10.30
  • 발행 : 2013.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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).

키워드

참고문헌

  1. Brill, P. H. and Posner, M. J. M. (1977). Level crossings in point processes applied to queue: Singlesever case, Operations Research, 25, 662-674. https://doi.org/10.1287/opre.25.4.662
  2. Dickson, D. C. M. and Willmot, G. E. (2005). The density of the time to ruin in the classical Poisson risk model, Astin Bulletin, 35, 45-60. https://doi.org/10.2143/AST.35.1.583165
  3. Gerber, H. U. (1990). When does the surplus reach a given target?, Insurance: Mathematics and Economics, 9, 115-119. https://doi.org/10.1016/0167-6687(90)90022-6
  4. Gerber, H. U. and Shiu, E. S. W. (1997). The joint distribution of the time of ruin, the surplus immediately before ruin and the deficit at ruin, Insurance: Mathematics and Economics, 21, 129-137. https://doi.org/10.1016/S0167-6687(97)00027-9
  5. Jeong, M. O. and Lee, E. Y. (2010). Optimal control of the surplus in an insurance policy, Journal of the Korean Statistical Society, 39, 431-437. https://doi.org/10.1016/j.jkss.2009.09.002
  6. Jeong, M. O., Lim, K. E. and Lee, E. Y. (2009). An optimization of a continuous time risk process, Applied Mathematical Modelling, 33, 4062-4068. https://doi.org/10.1016/j.apm.2009.02.007
  7. Klugman, S. A., Panjer, H. H. andWillmot, G. E. (2004). Loss Models: From Data to Decisions, John Wiley & Sons, Hoboken.

피인용 문헌

  1. Stationary distribution of the surplus process in a risk model with a continuous type investment vol.23, pp.5, 2016, https://doi.org/10.5351/CSAM.2016.23.5.423
  2. Stationary analysis of the surplus process in a risk model with investments vol.25, pp.4, 2014, https://doi.org/10.7465/jkdi.2014.25.4.915
  3. Surplus Process Perturbed by Diffusion and Subject to Two Types of Claim vol.22, pp.1, 2015, https://doi.org/10.5351/CSAM.2015.22.1.095
  4. An optimal continuous type investment policy for the surplus in a risk model vol.25, pp.1, 2018, https://doi.org/10.29220/CSAM.2018.25.1.091