Precise large deviations for random sums of END real-valued random variables with consistent variation
نویسندگان
چکیده
منابع مشابه
Extended Precise Large Deviations of Random Sums in the Presence of END Structure and Consistent Variation
The study of precise large deviations of random sums is an important topic in insurance and finance. In this paper, extended precise large deviations of random sums in the presence of END structure and consistent variation are investigated. The obtained results extend those of Chen and Zhang 2007 and Chen et al. 2011 . As an application, precise large deviations of the prospectiveloss process o...
متن کاملPrecise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation
The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (2006) and Liu (2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued random variables, are negatively dependent ...
متن کاملPrecise Large Deviations for Sums of Random Variables with Consistently Varying Tails in Multi-risk Models
Assume that there are k types of insurance contracts in an insurance company. The ith related claims are denoted by {Xij , j ≥ 1}, i = 1, . . . , k. In this paper we investigate large deviations for both partial sums S(k; n1, . . . , nk) = ∑ki=1 ∑ni j=1 Xij and random sums S(k; t) = ∑ki=1 ∑Ni(t) j=1 Xij , whereNi(t), i = 1, . . . , k, are counting processes for the claim number. The obtained re...
متن کاملPrecise Large Deviations for Sums of Random Variables with Consistently Varying Tails
Let {Xk, k ≥ 1} be a sequence of independent, identically distributed nonnegative random variables with common distribution function F and finite expectation μ > 0. Under the assumption that the tail probability F(x) = 1−F(x) is consistently varying as x tends to infinity, this paper investigates precise large deviations for both the partial sums Sn and the random sums SN(t), where N(·) is a co...
متن کاملLarge deviations for sums of partly dependent random variables
We use and extend a method by Hoeffding to obtain strong large deviation bounds for sums of dependent random variables with suitable dependency structure. The method is based on breaking up the sum into sums of independent variables. Applications are given to U -statistics, random strings and random graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.02.002