In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investment goal. This strategy favorably shapes the entire probability distribution of returns, as it simultaneously seeks a desired expected return, cuts off downside risk and implicitly caps volatility and higher moments. To illustrate the effectiveness of this investment strategy, we study a multiperiod portfolio optimization problem with transaction costs and develop a two-stage regression approach that improves the classical least squares Monte Carlo (LSMC) algorithm when dealing with difficult payoffs, such as highly concave, abruptly changing or discontinuous functions. Our numerical results show substantial improvements over the classical LSMC algorithm for both the constant relative risk-aversion (CRRA) utility approach and the proposed skewed target range strategy (STRS). Our numerical results illustrate the ability of the STRS to contain the portfolio value within the targeted range. When compared with the CRRA utility approach, the STRS achieves a similar mean-variance efficient frontier while delivering a better downside risk-return trade-off.

中文翻译：

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使用两阶段最小二乘蒙特卡罗方法进行多周期投资组合优化的偏斜目标范围策略

在本文中，我们为投资组合优化问题提出了一种新的投资策略。所提出的策略最大化了在目标范围内的预期投资组合价值，该范围由代表资本保护需求的保守下目标和代表投资目标的理想上目标组成。该策略有利地塑造了回报的整个概率分布，因为它同时寻求期望的预期回报，切断下行风险并隐含地限制波动性和更高的时刻。为了说明这种投资策略的有效性，我们研究了具有交易成本的多周期投资组合优化问题，并开发了一种两阶段回归方法，该方法在处理困难的收益（例如高凹、突然改变或不连续的功能。我们的数值结果表明，对于恒定相对风险规避 (CRRA) 效用方法和建议的偏斜目标范围策略 (STRS)，经典 LSMC 算法有了实质性改进。我们的数值结果说明了 STRS 将投资组合价值包含在目标范围内的能力。与 CRRA 效用方法相比，STRS 实现了类似的均值方差有效边界，同时提供了更好的下行风险回报权衡。我们的数值结果说明了 STRS 将投资组合价值包含在目标范围内的能力。与 CRRA 效用方法相比，STRS 实现了类似的均值方差有效边界，同时提供了更好的下行风险回报权衡。我们的数值结果说明了 STRS 将投资组合价值包含在目标范围内的能力。与 CRRA 效用方法相比，STRS 实现了类似的均值方差有效边界，同时提供了更好的下行风险回报权衡。