Figure 1.1. A sample path of {U(t), t ≥ 0}.
References
- Brill, P. H. and Posner, M. J. M. (1977). Level crossings in point processes applied to queue: single sever case, Operations Research, 25, 662-674. https://doi.org/10.1287/opre.25.4.662
- Cho, E. Y., Choi, S. K., and Lee, E. Y. (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
- Cho, Y. H., Choi, S. K., and Lee, E. Y. (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
- Choi, S. K. and Lee, E. Y. (2018). An optimal continuous type investment policy for the surplus in a risk model, Communications for Statistical Applications and Methods, 25, 91-97. https://doi.org/10.29220/CSAM.2018.25.1.091
- 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/10.1017/S0515036100014057
- Dvoretzky, A., Kiefer, J., and Wolfowitz, J. (1953). On the optimal character of the (s, S) policy in inventory theory, Econometrica, 21, 586-596. https://doi.org/10.2307/1907924
- Gerber, H. U. (1990). When does the surplus reach a given target? Insurance: Mathematics & Economics, 9, 115-119. https://doi.org/10.1016/0167-6687(90)90022-6
- 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 & Economics, 21, 129-137. https://doi.org/10.1016/S0167-6687(97)00027-9
- Karlin, S. and Taylor, H. M. (1975).A First Course in Stochastic Processes (2nd ed), Academic Press, New York.
- Kim, S. and Lee, E. Y. (2015). Stationary distribution of the surplus in a risk model with dividends and reinvestments, Journal of the Korean Statistical Society, 44, 516-529. https://doi.org/10.1016/j.jkss.2015.01.005
- Klugman, S. A., Panjer, H. H., and Willmot, G. E. (2004). Loss Models: From Data to Decisions (2nd ed), John Wiley & Sons, Hoboken, NJ.
- Ross, S. M. (1996). Stochastic Processes (2nd ed), John Wiley & Sons, New York.