We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circ...We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circular unitary ensembles. The corresponding Berry-Esseen bounds and Cram6r type moderate deviations are established. Our method is based on the estimates of corresponding cumulants. Numerical simulations are also presented to illustrate the theoretical results.展开更多
We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt, Zt, t ∈ [0, T], are two uncorrela...We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt, Zt, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log Sn （or log ｜Sn｜ in case Sn is negative） are obtained as n → ∞ under different discretization schemes for the asset price process St and the volatility process σt. Numerical simulations are presented to compare the convergence speeds in different schemes.展开更多
文摘We study the asymptotic behavior for log-determinants of two unitary but non-Hermitian random matrices： the spherical ensembles A-1B, where A and B are independent complex Ginibre ensembles and the truncation of circular unitary ensembles. The corresponding Berry-Esseen bounds and Cram6r type moderate deviations are established. Our method is based on the estimates of corresponding cumulants. Numerical simulations are also presented to illustrate the theoretical results.
基金Hui JIANG was Foundation of China （Grant No. 11771209） supported by the National Natural Science and the China Postdoctoral Science Foundation （Grant No. 2013M531341, 2016T90450） Shaochen WANG was supported by the Fundamental Research Funds for the Central Universities （Grant No. 2017BQ108）.
文摘We consider the Euler-Maruyama discretization of stochastic volatility model dSt = σtStdWt, dσt = ωσtdZt, t ∈ [0, T], which has been widely used in financial practice, where Wt, Zt, t ∈ [0, T], are two uncorrelated standard Brownian motions. Using asymptotic analysis techniques, the moderate deviation principles for log Sn （or log ｜Sn｜ in case Sn is negative） are obtained as n → ∞ under different discretization schemes for the asset price process St and the volatility process σt. Numerical simulations are presented to compare the convergence speeds in different schemes.
