| 孔繁超,赵朋.广义复合二项风险模型的若干大偏差结果[J].数学研究及应用,2009,29(6):1047~1053 |
| 广义复合二项风险模型的若干大偏差结果 |
| Some Large Deviation Results for Generalized Compound Binomial Risk Models |
| 投稿时间：2007-01-10 修订日期：2008-04-16 |
| DOI：10.3770/j.issn:1000-341X.2009.06.014 |
| 中文关键词: 广义复合二项风险模型 大偏差 重尾分布 破产概率. |
| 英文关键词:generalized compound binomial risk model large deviations heavy-tailed distribution ruin probability. |
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| 中文摘要: |
| 本文进一步研究[1]中的广义复合二项风险模型,把$\overline{F}\in ERV$的情形推广至$\overline{F}\in C$,得到了与[1]中相应的若干大偏差结果.这些结果可以应用于金融和保险中的某些具体问题. |
| 英文摘要: |
| This paper is a further investigation of large deviation for partial and random sums of random variables, where $\{X_{n},n\geq 1\}$ is non-negative independent identically distributed random variables with a common heavy-tailed distribution function $F$ on the real line $R$ and finite mean $\mu\in R$. $\{N(n),n\geq 0\}$ is a binomial process with a parameter $p\in(0,1)$ and independent of $\{X_{n},n\geq 1\}$; $\{M(n),n\geq 0\}$ is a Poisson process with intensity $\lambda>0$, $S_{n}=\sum_{i=1}^{N(n)}X_{i}-cM(n)$. Suppose $F\in C$, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance. |
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