Ruin problems with stochastic premium stochastic return on investments

被引：3

作者：

Wang R. ^{[1
]}

Xu L. ^{[1
,2
]}

Yao D. ^{[1
]}

机构：

[1] Department of Statistics, East China Normal University

[2] School of Mathematics and Computer Science, Anhui Normal University

来源：

Frontiers of Mathematics in China | 2007年 / 2卷 / 3期

基金：

中国国家自然科学基金;

关键词：

Expected discounted penalty function; Integro-differential equation; Lévy process; Martingale method; Ruin probability; Stochastic premium income;

D O I：

10.1007/s11464-007-0029-y

中图分类号：

学科分类号：

摘要：

In this paper, ruin problems in the risk model with stochastic premium incomes and stochastic return on investments are studied. The logarithm of the asset price process is assumed to be a Lévy process. An exact expression for expected discounted penalty function is established. Lower bounds and two kinds of upper bounds for expected discounted penalty function are obtained by inductive method and martingale approach. Integro-differential equations for the expected discounted penalty function are obtained when the Lévy process is a Brownian motion with positive drift and a compound Poisson process, respectively. Some analytical examples and numerical examples are given to illustrate the upper bounds and the applications of the integro-differential equations in this paper. © 2007 Higher Education Press and Springer-Verlag.

引用

页码：467 / 490

页数：23

共 15 条

[11]

Gerber H.U., Shiu E.S.W., The joint distribution of the time of ruin, the surplus immediatly before ruin, and the deficit at ruin, Insurance Math Econom, 21, pp. 129-137, (1997)

[12]

Cai J., Dickson D.C.M., On the expected discounted penalty function at ruin of a surplus process with interest, Insurance Math Econom, 30, pp. 389-404, (2002)

[13]

Grandell J., Aspects of Risk Theory, (1991)

[14]

Cai J., Dickson D.C.M., Upper bounds for ultimate ruin probabilities in the Sparre Andersen model with interest, Insurance Math Econom, 32, pp. 61-71, (2003)

[15]

Dufresne F., Gerber H.U., Risk theory for the compound Poisson process that is perturbed by diffusion, Insurance Math Econom, 10, pp. 51-59, (1991)

← 1 2 →