Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory. (English) Zbl 1112.62123

Wang, Dingcheng; Su, Chun; Zeng, Yong

Sci. China, Ser. A 48, No. 10, 1379-1394 (2005).

Summary: This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent on each other. Then the applications to ruin probabilities in a discrete time risk model with dependent stochastic returns are considered.

MSC:

62P05	Applications of statistics to actuarial sciences and financial mathematics
91B30	Risk theory, insurance (MSC2010)
62G32	Statistics of extreme values; tail inference
62G05	Nonparametric estimation

Keywords:

dependent stochastic return; discount factor; heavy-tails; discrete time insurance risk model; maxima of randomly weighted sums; ruin probability; tail probabilities; uniformly asymptotic estimate