Precise Large Deviation Probability For Random Sums And Its Applications

In this thesis, We study local large deviation result for random sums of independent andidentically distributed random variables. This thesis is divided into two chapters.In chapter 1, we introduce some important heavy-tailed distribution classes and review theresearch achievements on large deviation in recent years. Then, we introduce the main results inthis thesis.In chapter2, We prove local large deviation result for the random sum S(t) = Ni=(1t )ξi underthe condition F∈S, where {ξi,i≥1} be a sequence of independent identically distributedrandom variables with common distribution F and {N(t),t≥0} be a Possion process independentof {ξi,i≥1} . We also discuss its applications in surplus process and reinsurance.