The Finite-time Ruin Probability Of A Renewal Risk Model With An Exponential Lévy Process

In this paper, we study the discounted net loss process with an exponential Levy process as randomly weighted sum; we derive an asymptotic relation for the finite-time ruin probability with heavy-tailed claim in the renewal risk model introduced in this paper.In the renewal risk model, this paper proves the asymptotic relation as: hold when the claim size distribution belongs to the class ERV.We also obtain the asymptotic relation when the claim size distribution is extended to the class L∩D.In this renewal risk model, we obtain the uniform asymptotic estimate for the finite-time ruin probability as: hold when the claim size distribution belongs to both the classes ERV and L∩D.