Asymptotic Analysis of Ruin in Cev Model
نویسنده
چکیده
We give asymptotic analysis for probability of absorbtion P(τ0 ≤ T ) on the interval [0, T ], where τ0 = inf{t : Xt = 0} and Xt is a nonnegative diffusion process relative to Brownian motion Bt, dXt = μXtdt+ σX γ t dBt. X0 = K > 0 Diffusion parameter σx , γ ∈ [ 1 2 , 1) is not Lipschitz continuous and assures P(τ0 > T ) > 0. Our main result: lim K→∞ 1 K2(1−γ) logP(τ0 ≤ T ) = − 1 2EM T , where MT = R T 0 σ(1− γ)edBs. Moreover we describe the most likely path to absorbtion of the normed process Xt K for K → ∞.
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