RUIN PROBABILITIES VIA LOCAL ADJUSTMENT COEFFICIENTS

被引:14
作者
ASMUSSEN, S [1 ]
NIELSEN, HM [1 ]
机构
[1] BALTICA INSURANCE CO, COPENHAGEN, DENMARK
关键词
FAST SIMULATION; LARGE DEVIATIONS; LUNDBERG INEQUALITY; MARTINGALE; RARE EVENTS; SLOW MARKOV WALK; STORAGE PROCESS;
D O I
10.2307/3215126
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
Let psi(u) be the ruin probability in a risk process with initial reserve u, Poisson arrival rate beta, claim size distribution B and premium rate p(x) at level x of the reserve. Let gamma(x) be the non-zero solution of the local Lundberg equation beta(B[gamma(x)]-1)-gamma(x)p(x)=0 and I(u)=integral(0)(u) gamma(x)dx. It is shown that psi(u)less than or equal to e(-I(u)) provided p(x) is non-decreasing and that log psi(u)approximate to-I(u) in a slow Markov walk limit. Though the results and conditions are of large deviations type, the proofs are elementary and utilize piecewise comparisons with standard risk processes with a constant p. Also simulation via importance sampling using local exponential change of measure defined in terms of the gamma(x) is discussed and some numerical results are presented.
引用
收藏
页码:736 / 755
页数:20
相关论文
共 28 条
[1]  
[Anonymous], 1994, MARKOV CHAINS STOCHA
[3]   CONJUGATE PROCESSES AND THE SIMULATION OF RUIN PROBLEMS [J].
ASMUSSEN, S .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1985, 20 (02) :213-229
[4]  
ASMUSSEN S, 1989, ADV APPL PROBAB, V20, P913
[5]  
ASMUSSEN S, 1995, RUIN PROBABILITIES
[6]  
Asmussen S, 1991, INSUR MATH ECON, V10, P259
[7]  
ASMUSSEN S, 1995, FRONTIERS QUEUEING
[8]  
Bucklew J. A., 1990, LARGE DEVIATION TECH
[9]   LARGE DEVIATIONS AND RARE EVENTS IN THE STUDY OF STOCHASTIC ALGORITHMS [J].
COTTRELL, M ;
FORT, JC ;
MALGOUYRES, G .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1983, 28 (09) :907-920
[10]  
DASSIOS A, 1989, COMM STATIST STOCHAS, V5, P181