In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann bo...In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see <a href="#ref1">[1]</a>). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our 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In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see <a href="#ref1">[1]</a>). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our 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.
