Asymptotic analysis of ruin in the constant elasticity of variance model

We give an asymptotic analysis for the probability of absorption P(tau(0) 0. tau(0) = inf t : X(t) = 0 , and the parameter gamma is an element of [1/2, 1) in the diffusion coefficient sigma x(gamma) assures P(tau(0) 0. Our main result is lim(K ->infinity) 1/K(2)(1-gamma) log P(tau(0) infinity.