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1.
该文考虑变保费率的扰动风险模型,其中索赔的分布是重尾的.对这个风险模型,给出了索赔剩余过程的精细大偏差;同时,还得到了它的有限时间破产概率的Cramér-Lundberg型极限结果.  相似文献
2.
李克文  胡亦钧 《数学杂志》2002,22(2):131-139
本文研究了一类独立重尾随机变量随机和S(t)∧=∑k=1^N(t)Xk,t≥0的大偏差概率,其中{N(t),t≥0}是一放大晨负整数值随机变量;{Xn,n≥1}是非负,独立随机变量序列,并与{N(t),t≥0}独立。本文的结果将{Xn,n≥1}为独立同分布情形推广到了独立不同分布情形。  相似文献
3.
In this paper, we obtain results on precise large deviations for non-random and random sums of negatively associated nonnegative random variables with common dominatedly varying tail distribution function. We discover that, under certain conditions, three precise large-deviation prob- abilities with different centering numbers are equivalent to each other. Furthermore, we investigate precise large deviations for sums of negatively associated nonnegative random variables with certain negatively dependent occurrences. The obtained results extend and improve the corresponding results of Ng, Tang, Yan and Yang (J. Appl. Prob., 41, 93-107, 2004).  相似文献
4.
研究了服从长尾分布族上的随机变量和的精确大偏差问题,其中假设代表索赔额的随机变量序列是一列宽上限相依的、不同分布的随机变量序列。在给定一些假设条件下,得到了部分和与随机和的两种一致渐近结论。  相似文献
5.
We investigate the precise large deviations of random sums of negatively dependent random variables with consistently varying tails. We find out the asymptotic behavior of precise large deviations of random sums is insensitive to the negative dependence. We also consider the generalized dependent compound renewal risk model with consistent variation, which including premium process and claim process, and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.  相似文献
6.
研究形如$\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}$的非随机和的差的精确大偏差, 其中$\{X_{1j},j\geq 1\}$是一列服从共同分布$F_{1}(x)$ 的负相协随机变量序列, $\sum_{j=1}^{n_1(t)}X_{1j}$是$\{X_{1j},j\geq 1\}$的非随机和, $\{X_{2j},j\geq 1\}$是一列服从独立同分布的随机变量序列, $\sum_{j=1}^{n_2(t)}X_{2j}$是$\{X_{2j},j\geq 1\}$的非随机和, $n_1(t)$和$n_2(t)$是两个取正整数的函数. 在一些其它的条件下,得到了如下一致渐近关系$$\lim_{t\rightarrow\infty}\sup_{x\geq\gamma (n_{1}(t))^{p+1}}|\frac{P(\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}-(\mu_{1}n_{1}(t)-\mu_{2}n_{2}(t))>x)}{ n_{1}(t)\bar{F_{1}}(x)}-1|=0.$$  相似文献
7.
In this paper, we study the case of independent sums in multi-risk model. Assume that there exist k types of variables. The ith are denoted by (Xij,j ≥ 1), which are i.i.d. with common density function fi(x) ∈ OR and finite mean, i =- 1,., k. We investigate local large deviations for partial sums ∑i=1^k Sni=∑i=1^k ∑j=1^ni Xij.  相似文献
8.
Let $\{X,X_k: k\geq1\}$ be a sequence of independent and identically distributed random variables with a common distribution $F$. In this paper, the authors establish some results on the local precise large and moderate deviation probabilities for partial sums $S_n=\sum\limits_{i=1}^nX_i$ in a unified form in which $X$ may be a random variable of an arbitrary type, which state that under some suitable conditions, for some constants $T>0,\ a$ and $\tau>\frac12$ and for every fixed $\gamma>0$, the relation \begin{align*} P(S_n-na\in (x,x+T])\sim n F((x+a,x+a+T]) \end{align*} holds uniformly for all $x\geq \gamma n^{\tau}$ as $n\to\infty$, that is, \begin{align*} \lim_{n\to+\infty}\sup_{x\geq \gamma n^\tau}\Big|\frac{P(S_n-na\in (x,x+T])}{n F((x+a,x+a+T])}-1\Big|=0. \end{align*} The authors also discuss the case where $X$ has an infinite mean.  相似文献
9.
In this paper,we propose a customer-based individual risk model,in which potential claims by customers are described as i.i.d.heavy-tailed random variables,but different insurance policy holders are allowed to have different probabilities to make actual claims.Some precise large deviation results for the prospective-loss process are derived under certain mild assumptions,with emphasis on the case of heavy-tailed distribution function class ERV(extended regular variation).Lundberg type limiting results on the finite time ruin probabilities are also investigated.  相似文献
10.
The purpose of this note is to correct an error in Baltrunas et al. (2004) [1], and to give a more detailed argument to a formula whose validity has been questioned over the years. These details close a gap in the proof of Theorem 4.1 as originally stated, the validity of which is hereby strengthened.  相似文献
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