Optimal quadratic quantization for numerics: the Gaussian case
Optimal quadratic quantization for numerics: the Gaussian case
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数值的最佳二次量化：高斯情况
DOI：
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发表时间：
2003
期刊：
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通讯作者：
J. Printems
中科院分区：
文献类型：
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作者：
G. Pagès;J. Printems
最近，最优量化在多维数值积分、多资产美式期权定价、控制理论和非线性滤波理论中得到了重新讨论。在这篇文章中，我们启发了一些数值方法，以便得到一维及更高维高斯分布的精确最优二次量化。重点研究了确定性情况下的牛顿法(d=1)和高维情况下的随机梯度法(d≥2)。给出了与随机梯度法步骤有关的一些启发式算法。最后，借用数学金融学中的数值例子来测试我们的高斯最优量化器的精度。
Optimal quantization has been recently revisited in multi-dimensional numerical integration, multi-asset American option pricing, control theory and nonlinear filtering theory. In this paper, we enlighten some numerical procedures in order to get some accurate optimal quadratic quantization of the Gaussian distribution in one and higher dimensions. We study in particular Newton method in the deterministic case (dimension d = 1) and stochastic gradient in higher dimensional case (d ≥ 2). Some heuristics are provided which concern the step in the stochastic gradient method. Finally numerical examples borrowed from mathematical finance are used to test the accuracy of our Gaussian optimal quantizers.