Some Large Deviation Results for Generalized Compound Binomial Risk Models

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.