On a Classical Risk Model with a Constant Dividend Barrier.
Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.
- Published Version
We consider a risk model with a constant dividend barrier. An explicit expression is obtained for the joint distribution of the surplus immediately prior to ruin and the deficit at ruin, discounted by the ruin time. Such an expression involves known results on the joint distribution
at ruin for a classical risk model with single premium rate. The joint distributions related to the time periods when dividends are paid are also discussed. In particular, a new expression is obtained for the expected present value of the total amount of dividend payments until ruin.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 10/04|
Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||Expected present value of total dividends until ruin; Joint distribution of the surplus involving ruin time; Risk model with a constant dividend barrier|
|Deposited On:||02 Jun 2010 16:22|
|Last Modified:||04 Nov 2016 22:58|
References:Asmussen, S., 2000. Ruin probabilities. Word Scientific.
Chiu, S., Yin, C., 2003. The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical
risk process perturbed by diffusion. Insurance: Mathematics and Economics 33, 59–66.
Dickson, D.C.M., Dos Reis, A.D.E., 1996. On the distribution of duration of negative surplus. Scandinavian
Actuarial Journal 2, 148–164.
Dickson D.C.M., Waters H.R., 2004. Some optimal dividends problems. Astin Bulletin 34, 49–74.
Dos Reis, A.D.E., 1993. How long is the surplus below zero? Insurance: Mathematics and Economics 12, 23–38.
Gerber, H.U., 1979. An introduction to mathematical risk theory. S.S. Huebner Foundation Monographs,
University of Pennsylvania.
Gerber, H.U., 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.
Gerber, H.U., Shiu, E.S.W., 1998. On the time value of ruin. North American Actuarial Journal 2, 48–78.
Gerber, H.U., Shiu, E.S.W., 2004. Optimal dividends: analysis with Brownian motion. North American
Actuarial Journal 8, 1–20.
Li, S., Garrido, J., 2004. On a class of renewal risk models with a constant dividend barrier. To appear in
Insurance: Mathematics and Economics.
Lin, X., Willmot, G.E., Drekic, S., 2003. The classical risk model with a constant dividend barrier: Analysis of the Gerber-Shiu discounted penalty function. Insurance: Mathematics and Economics 33, 551–566.
Schmidli H., 1999. On the distribution of the surplus prior and at ruin. Astin Bulletin 29, 227–244.
Wu R., Wang G., Wei L., 2003. Joint distributions of some actuarial random vectors containing the time of ruin. Insurance: Mathematics and Economics 33, 147–161.
Zhang, C., Wang, G., 2003. The joint density function of three characteristics on jump–diffusion risk process.
Insurance: Mathematics and Economics 32, 445–455.
Zhou, X., 2003. When does surplus reach a certain level before ruin? To appear in Insurance: Mathematics and Economics.
Zhou, X., 2004. Risk model with a two–step premium rate. Submitted
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