TY - JOUR
T1 - Asymptotic analysis of ruin in the constant elasticity of variance model
AU - Klebaner, F.
AU - Liptser, R.
PY - 2011
Y1 - 2011
N2 - We give an asymptotic analysis for the probability of absorption P(τ0 ≤ T) on the interval [0, T] of a nonnegative solution Xt of the following stochastic differential equation with respect to the Brownian motion Bt: dXt = μXt dt + σXγ t dBt, X0 = K > 0. τ0 = inf{t:Xt = 0}, and the parameter γ ∈ [1/2, 1) in the diffusion coefficient σxγ assures P(τ0 ≤ T) > 0. Our main result is lim, where dBs. Besides we describe the most likely path to absorption of the normed process Xt/K for K →∞.
AB - We give an asymptotic analysis for the probability of absorption P(τ0 ≤ T) on the interval [0, T] of a nonnegative solution Xt of the following stochastic differential equation with respect to the Brownian motion Bt: dXt = μXt dt + σXγ t dBt, X0 = K > 0. τ0 = inf{t:Xt = 0}, and the parameter γ ∈ [1/2, 1) in the diffusion coefficient σxγ assures P(τ0 ≤ T) > 0. Our main result is lim, where dBs. Besides we describe the most likely path to absorption of the normed process Xt/K for K →∞.
KW - CEV model
KW - Diffusion process
KW - Large deviations
KW - Most likely path to ruin
UR - http://www.scopus.com/inward/record.url?scp=79959316855&partnerID=8YFLogxK
U2 - 10.1137/S0040585X97984814
DO - 10.1137/S0040585X97984814
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AN - SCOPUS:79959316855
SN - 0040-585X
VL - 55
SP - 291
EP - 297
JO - Theory of Probability and its Applications
JF - Theory of Probability and its Applications
IS - 2
ER -