MEAN‐VARIANCE POLICY FOR DISCRETE‐TIME CONE‐CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND THE MINIMUM‐VARIANCE SIGNED SUPERMARTINGALE MEASURE
MEAN‐VARIANCE POLICY FOR DISCRETE‐TIME CONE‐CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND THE MINIMUM‐VARIANCE SIGNED SUPERMARTINGALE MEASURE
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DOI：
10.2139/ssrn.2410632
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发表时间：
2014-03
影响因子：
1.6
通讯作者：
Xiangyu Cui;Duan Li;Xun Li
中科院分区：
文献类型：
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作者：
Xiangyu Cui;Duan Li;Xun Li
离散时间均值方差投资组合选择公式是一般动态均值风险投资组合选择问题的代表，通常不满足时间一致性效率（TCIE），即，对于相应的截断问题，截断的预先提交的有效策略可能变得无效。在本文中，我们分析研究了投资组合约束对凸锥约束市场TCIE的影响。更具体地说，我们推导了预承诺有效均值方差策略和最小方差符号上鞅测度（VSSM）的半解析表达式，并研究了它们之间的关系。我们的分析表明，预先承诺的离散时间有效的均值方差策略满足TCIE当且仅当VSSM的密度的条件期望（相对于原始概率测度）是非负的，或者一旦条件期望变为负值，它保持相同的负值，直到终端时间。我们的研究结果表明，TCIE属性只取决于基本的市场环境，包括投资组合约束。这促使我们建立一个一般的程序，通过引入适当的投资组合约束条件，构建TCIE动态投资组合选择问题。
The discrete‐time mean‐variance portfolio selection formulation, which is a representative of general dynamic mean‐risk portfolio selection problems, typically does not satisfy time consistency in efficiency (TCIE), i.e., a truncated precommitted efficient policy may become inefficient for the corresponding truncated problem. In this paper, we analytically investigate the effect of portfolio constraints on the TCIE of convex cone‐constrained markets. More specifically, we derive semi‐analytical expressions for the precommitted efficient mean‐variance policy and the minimum‐variance signed supermartingale measure (VSSM) and examine their relationship. Our analysis shows that the precommitted discrete‐time efficient mean‐variance policy satisfies TCIE if and only if the conditional expectation of the density of the VSSM (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our finding indicates that the TCIE property depends only on the basic market setting, including portfolio constraints. This motivates us to establish a general procedure for constructing TCIE dynamic portfolio selection problems by introducing suitable portfolio constraints.