Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

Science in China, Series A: Mathematics

Volumn 48, Issue 10, 2005, Pages 1379-1394

  Wang, Dingcheng ^a   Su, Chun ^b   Zeng, Yong ^a  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

Dependent stochastic return; Discount factor; Discrete time insurance risk model; Heavy tails; Maxima of randomly weighted sums; Ruin probability; Tail probabilities; Uniformly asymptotic estimate

Indexed keywords

EID: 27544513160     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1360/022004-16     Document Type: Article

References (16)

1. Nyrhinen, H., On the ruin probabilities in a general economic environment, Stochastic Process. Appl., 1999, 83(2): 319-330.
2. Tang, Q., Tsitsiashvili, G., Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks, Stochastic Process. Appl., 2003, 108(2): 299-325.
3. Tang, Q., Tsitsiashvili, G., Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments, Adv. in Appl. Probab., 2004, 36(4): 1278-1299.
4. Cai, J., Discrete time risk models under rates of interest, Prob. Eng. Inf. Sci., 2002, 16: 309-324.
5. Wang, D. C., Tang, Q., Tail Probabilities of randomly weighted sums of random variables with dominated variation, Stochastic Models, 2006, 22(2), to appear.
6. Bingham, N. H., Goldie, C. M., Teugels, J. L., Regular Variation, Cambridge: Cambridge University Press, 1987.
7. Jelenkovć, P. R., Lazar, A. A., Asymptotic results for multiplexing subexponential on-off processes, Adv. Appl. Prob., 1999, 31: 394-421.
8. Schlegel, S., Ruin probabilities in perturbed risk models, Insurance: Mathematics and Economics, 1998, 22: 93-104.
9. Ng, K., Tang, Q., Yan, J. et al., Precise large deviations for sums of i.i.d. random variables with consistently varying tails, J. Appl. Prob., 2004, 41: 93-107.
10. Cai,J., Tang, Q., On max-sum-equivalence and convolution closure of heavy-tailed distributions and their applications, J. Appl. Probab., 2004, 41: 117-130.
11. Daley, D. J., The moment index of minima, J. Appl. Probab., 2001, 38A: 33-36.
12. Cline, D. B. H., Samorodnitsky, G., Subexponentiality of the product of independent random variables, Stochastic Process. Appl., 1994, 49(1): 75-98.
13. Paulsen, J., Ruin theory with compounding assets- a survey, Insurance: Math. Econom., 1998, 22: 3-16.
14. Cai, J., Dickson, D.C. M., Ruin probabilities with a Markov chain interest model, Insurance: Mathematics and Economics, 2004, 35: 513-525.
15. Cai, J., Ruin probabilities with dependent rates of interest, J. Appl. Probab.,2002, 39: 312-323.
16. Breiman, L., On some limit theorems similar to the arc-sin law, Theor. Probability Appl., 1965, 10: 323-331.