Preservation of Scalarization Optimal Points in the Embedding Technique for Continuous Time Mean Variance Optimization
Preservation of Scalarization Optimal Points in the Embedding Technique for Continuous Time Mean Variance Optimization
复制标题
连续时间均方差优化嵌入技术中标量化最优点的保存
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Yuying Li
中科院分区：
文献类型：
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作者：
S. Tse;P. Forsyth;Yuying Li
连续时间均值方差(MV)问题优化了双目标准则$(数学V，数学E)$，分别表示随机变量在时间范围$T$结束时的方差$数学V$和期望值$数学E$。这个问题在计算上具有挑战性，因为动态规划原理不能直接应用于方差准则。一种嵌入技术已在[D.Li和W.L.Ng，Math.《金融》，第10期(2000)，第387-406页；周晓云、李东达，应用。数学课。Optim.，42(2000)，pp.19--33]来生成MV标量化最优点的集合，其通常是MV Pareto最优点的子集。然而，当我们在数值算法的背景下应用嵌入技术时，有许多复杂的问题。具体地说，由嵌入技术产生的前沿可能包含不是MV最优的伪点。在本文中，我们提出了一种方法来消除这些点，当它们存在的时候。我们展示了原版MV..。
A continuous time mean variance (MV) problem optimizes the biobjective criteria $(mathcal V,mathcal E)$, representing variance $mathcal V$ and expected value $mathcal E$, respectively, of a random variable at the end of a time horizon $T$. This problem is computationally challenging since the dynamic programming principle cannot be directly applied to the variance criterion. An embedding technique has been proposed in [D. Li and W. L. Ng, Math. Finance, 10 (2000), pp. 387--406; X. Y. Zhou and D. Li, Appl. Math. Optim., 42 (2000), pp. 19--33] to generate the set of MV scalarization optimal points, which is in general a subset of the MV Pareto optimal points. However, there are a number of complications when we apply the embedding technique in the context of a numerical algorithm. In particular, the frontier generated by the embedding technique may contain spurious points which are not MV optimal. In this paper, we propose a method to eliminate such points, when they exist. We show that the original MV ...