It is discussed that how to choose {h{t),t≥ 0} and {J(t),t≥ 0} in the local large deviation result for the random sum S{t) = ∑N(t)ζii=1, t≥0 under the condition F∈S△, where △ = (0,T], T≤∞, and {N(t),t≥ 0} be a Possion process independent of {ζi,i}. Its applications in claim risk process and reinsurance treaties are also discussed.%研究了在F∈S△,Δ=(0,T],T≤∞的条件下随机和S(t)=N(t)∑i=1ζi,t≥0中心化的局部精细大偏差结果中{h(t),t≥0}和{J(t),t≥0}的选取,并且给出了随机和的局部精细大偏差在索赔过程和再保险中的应用.
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