Ruin probabilities of small noise jump-diffusions with heavy tails

Let X-epsilon(x) be a solution of a stochastic differential equation dX(t)(epsilon)=f (X-t(epsilon))dt+epsilon dL(t), X-0(epsilon)(x)=x>0, t is an element of [0, 1], where L is a Levy process with heavy tails. In the limit of the scale parameter epsilon down arrow 0 we determine the finite horizon ruin probability P(inf(t is an element of)[0, 1] X-t(epsilon)(x) <0). Copyright (c) 2007 John Wiley & Sons, Ltd.