Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
复制标题
一般条件下离散后向随机微分方程的线性回归MDP格式
DOI：
10.1090/mcom/3013
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Plamen Turkedjiev
中科院分区：
文献类型：
--
作者：
E. Gobet;Plamen Turkedjiev
我们设计了一种数值方案来求解由后向随机微分方程的时间离散化产生的多步前向动态规划（MDP）方程。假设生成器是局部 Lipschitz 生成器，其中包括一些二次驱动器的情况。当使用经验最小二乘回归计算大量条件期望序列时，在一般情况下，我们将上限误差建立为局部回归误差的平均值，而不是总和，这表明我们的误差估计是严格的。尽管存在嵌套回归问题，但相互依赖性错误被证明最多为统计回归错误的数量级（最多为对数因子）。最后，我们根据值函数的维度和平滑度，在网格大小趋近于零的时间限制内优化算法参数，并计算实现给定精度所需的复杂度。数值实验说明了理论收敛估计。
We design a numerical scheme for solving the Multi step-forward Dynamic Programming (MDP) equation arising from the time-discretization of backward stochastic differential equations. The generator is assumed to be locally Lipschitz, which includes some cases of quadratic drivers. When the large sequence of conditional expectations is computed using empirical least-squares regressions, under general conditions we establish an upper bound error as the average, rather than the sum, of local regression errors only, suggesting that our error estimation is tight. Despite the nested regression problems, the interdependency errors are justified to be at most of the order of the statistical regression errors (up to logarithmic factor). Finally, we optimize the algorithm parameters, depending on the dimension and on the smoothness of value functions, in the limit as the time mesh size goes to zero and compute the complexity needed to achieve a given accuracy. Numerical experiments are presented illustrating theoretical convergence estimates.
后向 SDE 的重要性采样
影响因子：
1.3
作者：
Bender;Moseler
通讯作者：
Moseler
影响因子：
1.4
作者：
Christian Bender;R. Denk
通讯作者：
Christian Bender;R. Denk