Some Large Deviation Results for Generalized Compound Binomial Risk Models
Received:January 10, 2007  Revised:April 16, 2008
Key Words: generalized compound binomial risk model   large deviations   heavy-tailed distribution   ruin probability.  
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Author NameAffiliation
KONG Fan Chao School of Mathematics, Anhui University, Anhui 230039, China 
ZHAO Peng School of Mathematics, Anhui University, Anhui 230039, China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.06.014
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