论文标题
尖锐的$ l^1 $ - log-heston sde的approximation by euler-type方法
Sharp $L^1$-Approximation of the log-Heston SDE by Euler-type methods
论文作者
论文摘要
我们通过Euler-Type方法在等距的时间点研究log-heston SDE的$ l^1 $ apptroximation。如果基本CIR流程的feller索引$ν$满足$ν> 1 $，我们将建立$1/2-ε$ for $ε> 0 $ $ 1/2-ε$。因此，我们恢复具有全球Lipschitz系数的SDE的EULER方案的标准收敛顺序。此外，我们讨论了$ν\ leq 1 $，并通过几个数字示例说明了我们的发现。
We study the $L^1$-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order $ 1/2-ε$ for $ε>0$ arbitrarily small, if the Feller index $ν$ of the underlying CIR process satisfies $ν> 1$. Thus, we recover the standard convergence order of the Euler scheme for SDEs with globally Lipschitz coefficients. Moreover, we discuss the case $ν\leq 1$ and illustrate our findings by several numerical examples.
