多期投资组合选择问题的一个闭式解 二次效用函数

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摘要翻译：
本文给出了具有无风险资产和无风险资产的二次效用函数的多期投资组合选择问题的一个闭式解。所有结果都是在弱条件下得到的。不需要对不同时间点之间的相关结构作任何假设，也不需要对分布作任何假设。所有的表达式都是用条件均值向量和条件协方差矩阵表示的。如果资产收益的多元过程是独立的，则在不存在无风险资产的情况下，解表示为通过求解单期Markowitz优化问题得到的最优投资组合权重序列。过程动力学仅包含在效用函数的形状参数中。如果存在无风险资产，则多期最优投资组合权重与单期解乘以依赖于过程动力学的时变常数成正比。值得注意的是，在相切投资组合的情况下，多周期解与简单周期解的序列一致。最后，针对实际数据，我们将所建议的策略与现有的多期投资组合配置方法进行了比较。
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英文标题：
《A Closed-Form Solution of the Multi-Period Portfolio Choice Problem for
  a Quadratic Utility Function》
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作者：
Taras Bodnar, Nestor Parolya and Wolfgang Schmid
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最新提交年份：
2014
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Portfolio Management        项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
--

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英文摘要：
  In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No assumption on the correlation structure between different time points is needed and no assumption on the distribution is imposed. All expressions are presented in terms of the conditional mean vectors and the conditional covariance matrices. If the multivariate process of the asset returns is independent it is shown that in the case without a riskless asset the solution is presented as a sequence of optimal portfolio weights obtained by solving the single-period Markowitz optimization problem. The process dynamics are included only in the shape parameter of the utility function. If a riskless asset is present then the multi-period optimal portfolio weights are proportional to the single-period solutions multiplied by time-varying constants which are depending on the process dynamics. Remarkably, in the case of a portfolio selection with the tangency portfolio the multi-period solution coincides with the sequence of the simple-period solutions. Finally, we compare the suggested strategies with existing multi-period portfolio allocation methods for real data.
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PDF链接：
https://arxiv.org/pdf/1207.1003

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关键词：投资组合选择 选择问题 效用函数 投资组合 Optimization 单期 权重 多期 需要 动力学