Present value distributions with applications to ruin theory and stochastic equations

被引：60

作者：

Gjessing, HK

Paulsen, J

机构：

[1] UNIV BERGEN, DEPT MATH, N-5008 BERGEN, NORWAY

[2] HAUKELAND HOSP, AHH, DIV MED STATE, N-5021 BERGEN, NORWAY

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1997年 / 71卷 / 01期

关键词：

present value distribution; ruin probability; stochastic equation; integro-differential equation; characteristic function; Laplace transform;

D O I：

10.1016/S0304-4149(97)00072-0

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：

We study the distribution of the stochastic integral integral(0)(infinity) e(-Rt) dP(t) where P and R are independent Levy processes with a finite number of jumps on finite time intervals. The exact distribution is obtained in many special cases, and we derive asymptotic properties of the tails of the distributions in the general case. These results are applied to give two new examples of exact solutions of the probability of eventual ruin of an insurance portfolio where return on investments are stochastic. Finally we use the results to give new examples of exact solutions of the stochastic equations Z =(d) AZ + B and Z =(d) A(Z + C) where Z and (A,B) (or (A, C)) are independent. (C) 1997 Elsevier Science B.V.

引用

页码：123 / 144

页数：22

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