Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.
JIANG Tao School of Finance, Zhejiang Gongshang University, Hangzhou 310018, China
Let {Xt,t0} be a Lévy process with Lévy measure ν on(∞,∞),and let τ be a nonnegative random variable independent of {Xt,t0}.We are interested in the tail probabilities of X τ and X(τ) = sup0≤t≤τXt.For various cases,under the assumption that either the Lévy measure ν or the random variable τ has a heavy right tail we prove that both Pr(X τ > x) and Pr(X(τ) > x) are asymptotic to Eτν((x,∞)) + Pr(τ > x/(0 ∨ EX 1)) as x →∞,where Pr(τ > x/0) = 0 by convention.
