SIAM Journal on Financial Mathematics, Volume 12, Issue 2, Page 566-603, January 2021.
We compare the distributions of terminal wealth obtained from implementing the optimal investment strategies associated with the different approaches to dynamic mean-variance (MV) optimization available in the literature. This includes the precommitment MV (PCMV) approach, the dynamically optimal MV (DOMV) approach, as well as the time-consistent MV approach with a constant risk aversion parameter (cTCMV) and wealth-dependent risk-aversion parameter (dTCMV), respectively. For benchmarking purposes, a constant proportion (CP) investment strategy is also considered. To ensure that terminal wealth distributions are compared on a fair and practical basis, we assume that an investor, otherwise agnostic about the philosophical differences of the underlying approaches to dynamic MV optimization, requires that the same expected value of terminal wealth should be obtained regardless of the approach. We present first-order stochastic dominance results proving that for wealth outcomes below the chosen expected value target, the cTCMV strategy always outperforms the DOMV strategy, and an appropriately chosen CP strategy always outperforms the dTCMV strategy. We also show that the PCMV strategy results in a terminal wealth distribution with fundamentally different characteristics than any of the other strategies. Finally, our analytical results are very effective in explaining the numerical results currently available in the literature regarding the relative performance of the various investment strategies.

中文翻译：

---

动态均方差最优投资策略下的终端财富分配

SIAM 金融数学杂志，第 12 卷，第 2 期，第 566-603 页，2021 年 1 月。
我们比较了通过实施与文献中可用的动态均值方差 (MV) 优化的不同方法相关的最佳投资策略而获得的终端财富分布。这包括预先承诺 MV (PCMV) 方法、动态最优 MV (DOMV) 方法，以及具有恒定风险规避参数 (cTCMV) 和财富相关风险规避参数 (dTCMV) 的时间一致 MV 方法。 . 出于基准测试的目的，还考虑了恒定比例 (CP) 投资策略。为了确保在公平和实际的基础上比较终端财富分配，我们假设投资者不知道动态 MV 优化的基本方法的哲学差异，要求无论采用何种方法，都应获得相同的终端财富预期值。We present first-order stochastic dominance results proving that for wealth outcomes below the chosen expected value target, the cTCMV strategy always outperforms the DOMV strategy, and an appropriately chosen CP strategy always outperforms the dTCMV strategy. 我们还表明，PCMV 策略导致最终财富分配与任何其他策略具有根本不同的特征。最后，我们的分析结果非常有效地解释了目前文献中关于各种投资策略的相对表现的数值结果。We present first-order stochastic dominance results proving that for wealth outcomes below the chosen expected value target, the cTCMV strategy always outperforms the DOMV strategy, and an appropriately chosen CP strategy always outperforms the dTCMV strategy. 我们还表明，PCMV 策略导致最终财富分配与任何其他策略具有根本不同的特征。最后，我们的分析结果非常有效地解释了目前文献中关于各种投资策略的相对表现的数值结果。We present first-order stochastic dominance results proving that for wealth outcomes below the chosen expected value target, the cTCMV strategy always outperforms the DOMV strategy, and an appropriately chosen CP strategy always outperforms the dTCMV strategy. 我们还表明，PCMV 策略导致最终财富分配与任何其他策略具有根本不同的特征。最后，我们的分析结果非常有效地解释了目前文献中关于各种投资策略的相对表现的数值结果。我们还表明，PCMV 策略导致最终财富分配与任何其他策略具有根本不同的特征。最后，我们的分析结果非常有效地解释了目前文献中关于各种投资策略的相对表现的数值结果。我们还表明，PCMV 策略导致最终财富分配与任何其他策略具有根本不同的特征。最后，我们的分析结果非常有效地解释了目前文献中关于各种投资策略的相对表现的数值结果。