Tail probabilities of randomly weighted sums of random variables with dominated variation

Stochastic Models

Volumn 22, Issue 2, 2006, Pages 253-272

  Wang, Dingcheng ^a   Tang, Qihe ^b  

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

^b UNIVERSITY OF IOWA   (United States)

Author keywords

Heavy tail; Maximum of sums; Randomly weighted sums; Ruin probability; Stochastic return; Tail probability

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBABILITY; STOCHASTIC PROGRAMMING; WEIGHING;

HEAVY TAILS; MAXIMUM OF SUMS; RANDOMLY WEIGHTED SUMS; RUIN PROBABILITY; STOCHASTIC RETURN; TAIL PROBABILITY;

PROBABILISTIC LOGICS;

EID: 33646443053     PISSN: 15326349     EISSN: 15324214     Source Type: Journal    
DOI: 10.1080/15326340600649029     Document Type: Article

References (14)

1. Bingham, N.H.; Goldie, C.M.; Teugels, J.L. Regular Variation; Cambridge University Press: Cambridge, 1987.
2. Breiman, L. On some limit theorems similar to the arc-sin law. Teor. Verojatnost. i Primenen. 1965, 10, 351-360;
3. translation in Theor. Probability Appl. 1965, 10, 323-331.
4. Cai, J. Ruin probabilities with dependent rates of interest. J. Appl. Probab. 2002, 39 (2), 312-323.
5. Cline, D.B.H.; Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 1994, 49 (1), 75-98.
6. Embrechts, P.; Klüppelberg, C.; Mikosch, T. Modelling Extremal Events for Insurance and Finance; Springer-Verlag: Berlin, 1997.
7. Nyrhinen, H. On the ruin probabilities in a general economic environment. Stochastic Process. Appl. 1999, 83 (2), 319-330.
8. Nyrhinen, H. Finite and infinite time ruin probabilities in a stochastic economic environment. Stochastic Process. Appl. 2001, 92 (2), 265-285.
9. Resnick, S.I.; Willekens, E. Moving averages with random coefficients and random coefficient autoregressive models. Comm. Statist. Stochastic Models 1991, 7 (4), 511-525.
10. 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.
11. Tang, Q.; Tsitsiashvili, G. Randomly weighted sums of subexponential random variables with application to ruin theory Extremes 2003, 6 (3), 171-188.
12. 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.
13. Wang, D.C.; Su, C.; Zeng, Y. Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory. Sci. China Ser. A 2005, 48 (10), 1379-1394.
14. Goovaerts, M.J.; Kaas, R.; Laeven, R.J.A.; Tang, Q.; Vernic, R. The tail probability of discounted sums of Pareto-like losses in insurance. Scand. Actuar. J. 2005, 6, 446-461.