论文标题
$ l^1 $ - log-heston sde的订单屏障
The order barrier for the $L^1$-approximation of the log-Heston SDE at a single point
论文作者
论文摘要
我们通过任意使用驱动驾驶布朗尼运动的等距离散化的任意方法来研究终端时间点上log-heston sde的$ l^1 $ apptroximation。我们表明，此类方法最多可以实现$ \ min \ {ν，\ tfrac {1} {2} {2} \} $，其中$ν$是基础CIR进程的Feller索引。结果，欧拉型方案对于$ν\ geq 1 $是最佳的，因为它们具有收敛订单$ \ tfrac {1} {2} {2}-ε$，for $ε> 0 $在此制度中任意小。
We study the $L^1$-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order $ \min \{ ν, \tfrac{1}{2} \}$, where $ν$ is the Feller index of the underlying CIR process. As a consequence Euler-type schemes are optimal for $ν\geq 1$, since they have convergence order $\tfrac{1}{2}-ε$ for $ε>0$ arbitrarily small in this regime.
