DOI QR코드

DOI QR Code

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

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.

키워드

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.