Distributions for the risk process with a stochastic return on investments

被引：54
作者：
Wang, GJ [1 ]
Wu, R
机构：
[1] Suzhou Univ, Dept Math, Suzhou 215006, Peoples R China
[2] Nankai Univ, Dept Math, Tianjin 300071, Peoples R China
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2001年 / 95卷 / 02期
基金：
中国国家自然科学基金;
关键词：
risk process; ruin probability; integro-differential equation; surplus distribution at the time of ruin; supremum distribution before ruin;
D O I：
10.1016/S0304-4149(01)00102-8
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we consider a risk model with stochastic return on investments. We mainly discuss the min probability, the surplus distribution at the time of ruin and the supremum distribution of the surplus before ruin. We prove some properties for these distributions and derive the integro-differential equations satisfied by them. We present the relation between the ruin probability and the supremum distribution before ruin. (C) 2001 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：329 / 341
页数：13
相关论文
共 12 条
[1]   CLASSICAL RISK THEORY IN AN ECONOMIC-ENVIRONMENT [J].
DELBAEN, F ;
HAEZENDONCK, J .
INSURANCE MATHEMATICS & ECONOMICS, 1987, 6 (02) :85-116
[2]   Present value distributions with applications to ruin theory and stochastic equations [J].
Gjessing, HK ;
Paulsen, J .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1997, 71 (01) :123-144
[3]  
Harrison J.M., 1977, STOCHASTIC PROCESS A, V5, P67, DOI [10.1016/0304-4149(77)90051-5, DOI 10.1016/0304-4149(77)90051-5]
[4]  
Kl├a┬╝ppelberg C., 1998, SCAND ACTUAR J, V1998, P49, DOI [10.1080/03461238.1998.10413991, DOI 10.1080/03461238.1998.10413991]
[5]  
Nikiforov A. F., 1988, SPECIAL FUNCTION MAT
[6]   Ruin problems with assets and liabilities of diffusion type [J].
Norberg, R .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 81 (02) :255-269
[7]   RISK THEORY IN A STOCHASTIC ECONOMIC-ENVIRONMENT [J].
PAULSEN, J .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1993, 46 (02) :327-361
[8]   Ruin theory with stochastic return on investments [J].
Paulsen, J ;
Gjessing, HK .
ADVANCES IN APPLIED PROBABILITY, 1997, 29 (04) :965-985
[9]  
TAYLOR GC, 1979, ASTIN BULL, V16, P149
[10]  
WANG G, 1998, UNPUB INSURANCE MATH
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