Communications for Statistical Applications and Methods

  • 제25권1호
  • /
  • Pages.91-97
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  • 2018
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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An optimal continuous type investment policy for the surplus in a risk model

  • 투고 : 2017.10.17
  • 심사 : 2017.11.29
  • 발행 : 2018.01.31
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초록

In this paper, we show that there exists an optimal investment policy for the surplus in a risk model, in which the surplus is continuously invested to other business at a constant rate a > 0, whenever the level of the surplus exceeds a given threshold V > 0. We assign, to the risk model, two costs, the penalty per unit time while the level of the surplus being under V > 0 and the opportunity cost per unit time by keeping a unit amount of the surplus. After calculating the long-run average cost per unit time, we show that there exists an optimal investment rate $a^*$>0 which minimizes the long-run average cost per unit time, when the claim amount follows an exponential distribution.

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참고문헌

  1. Cho EY, Choi SK, and Lee EY (2013). Transient and stationary analyses of the surplus in a risk model, Communications for Statistical Applications and Methods, 20, 475-480. https://doi.org/10.5351/CSAM.2013.20.6.475
  2. Cho YH, Choi SK, and Lee EY (2016). Stationary distribution of the surplus process in a risk model with a continuous type investment, Communications for Statistical Applications and Methods, 23, 423-432. https://doi.org/10.5351/CSAM.2016.23.5.423
  3. Dickson DCM and Willmot GE (2005). The density of the time to ruin in the classical Poisson risk model, ASTIN Bulletin, 35, 45-60. https://doi.org/10.1017/S0515036100014057
  4. Dufresne F and Gerber HU (1991). Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance: Mathematics and Economics, 10, 51-59.
  5. Gerber HU (1990). When does the surplus reach a given target?, Insurance: Mathematics and Economics, 9, 115-119.
  6. Gerber HU and Shiu ESW (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
  7. Klugman SA, Panjer HH, and Willmot GE (2004). Loss Models: From Data to Decisions (2nd ed), John Wiley & Sons, Hoboken, NJ.
  8. Lim SE, Choi SK, and Lee EY (2016). An optimal management policy for the surplus process with investments, The Korean Journal of Applied Statistics, 29, 1165-1172.
  9. Ross SM (1996). Stochastic Processes (2nd ed), John Wiley & Sons, New York.