Asymptotic analysis of ruin in CEV model

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We give asymptotic analysis for probability of absorbtion P(τ₀≤ T) on the interval [0,T], where τ₀={t:Xₜ=0} and Xₜ is a nonnegative diffusion process relative to Brownian motion Bₜ, dXₜ&=μXₜdt+σXγₜdBₜ. X₀&=K>0 Diffusion parameter σxγ, γ∈ [1/2,1) is not Lipschitz continuous and assures P(τ₀>T)>0. Our main result: ₖ→∞ 1K²⁽¹⁻γ⁾(τ₀≤ T) =-1/2 M²ₜ, where Mₜ=∫₀ᵗσ(1-γ)e⁻⁽¹⁻γ⁾μˢdBₛ. Moreover we describe the most likely path to absorbtion of the normed process Xₜ/K for K→∞.