We study the optimal multi-period asset allocation problem with leverage constraints in a persistent, high-inflation environment. Based on filtered high-inflation regimes, we discover that a portfolio containing an equal-weighted stock index partially stochastically dominates a portfolio containing a capitalization-weighted stock index. Assuming the asset prices follow the jump diffusion model during high inflation periods, we establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective. The closed-form solution provides insights but requires unrealistic constraints. To obtain strategies under more practical considerations, we consider a constrained optimal control problem with bounded leverage. To solve this optimal control problem, we propose a novel leverage-feasible neural network (LFNN) model that approximates the optimal control directly. The LFNN model avoids high-dimensional evaluation of the conditional expectation (common in dynamic programming (DP) approaches). We establish mathematically that the LFNN approximation can yield a solution that is arbitrarily close to the solution of the original optimal control problem with bounded leverage. Numerical experiments show that the LFNN model achieves comparable performance to the closed-form solution on simulated data. We apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns. The LFNN strategy consistently outperforms the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the terminal date. These results suggest that during persistent inflation regimes, investors should favor short-term bonds over long-term bonds, and the equal-weighted stock index over the cap-weighted stock index.

翻译：我们研究在高通胀持续环境下带有杠杆约束的最优多期资产配置问题。基于过滤后的高通胀体制，我们发现包含等权股票指数的投资组合在部分随机占优意义上优于包含市值加权股票指数的投资组合。假设资产价格在高通胀时期服从跳跃扩散模型，我们建立了在累积二次跟踪差（CD）目标下优于被动策略的最优策略闭式解。该闭式解提供了见解，但需要不现实的约束条件。为获得更符合实际考虑的策略，我们考虑了带有杠杆约束的最优控制问题。为解决该最优控制问题，我们提出了一种新颖的杠杆可行神经网络（LFNN）模型，该模型直接逼近最优控制。LFNN模型避免了动态规划（DP）方法中常见的高维条件期望评估。我们从数学上证明了LFNN逼近能够产生与原始有界杠杆最优控制问题解任意接近的解。数值实验表明，在模拟数据上LFNN模型取得了与闭式解相当的性能。我们将LFNN方法应用于基于自助法重采样资产收益的四资产投资场景。LFNN策略始终以约200个基点（年化收益中位数）优于被动基准策略，在终端日期有超过90%的概率超越基准。这些结果表明，在持续通胀时期，投资者应偏好短期债券而非长期债券，并应选择等权股票指数而非市值加权股票指数。