Motivated by the current global high inflation scenario, we aim to discover a dynamic multi-period allocation strategy to optimally outperform a passive benchmark while adhering to a bounded leverage limit. To this end, we formulate an optimal control problem to outperform a benchmark portfolio throughout the investment horizon. Assuming the asset prices follow the jump-diffusion model during high inflation periods, we first establish a closed-form solution for the optimal strategy that outperforms a passive strategy under the cumulative quadratic tracking difference (CD) objective, assuming continuous trading and no bankruptcy. To obtain strategies under the bounded leverage constraint among other realistic constraints, we then propose a novel leverage-feasible neural network (LFNN) to represent control, which converts the original constrained optimization problem into an unconstrained optimization problem that is computationally feasible with standard optimization methods. 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. We further apply the LFNN approach to a four-asset investment scenario with bootstrap resampled asset returns from the filtered high inflation regime data. The LFNN strategy is shown to consistently outperform the passive benchmark strategy by about 200 bps (median annualized return), with a greater than 90% probability of outperforming the benchmark at the end of the investment horizon.

翻译：摘要：受当前全球高通胀背景的驱动，我们旨在发现一种动态多周期配置策略，在满足有限杠杆约束的同时，以最优方式超越被动基准。为此，我们构建了一个最优控制问题，以在整个投资期内超越基准投资组合。假设资产价格在高通胀时期遵循跳跃扩散模型，我们首先针对在连续交易且无破产假设下以累积二次跟踪差为目标的被动策略，推导出最优策略的闭式解。为在有限杠杆等现实约束下获得策略，我们进一步提出了一种新颖的杠杆可行神经网络（LFNN）来表示控制，将原始有约束优化问题转化为可采用标准优化方法进行计算的可行无约束优化问题。我们从数学上证明，LFNN近似能生成与原始带有限杠杆的最优控制问题解任意接近的解。我们进一步将LFNN方法应用于四资产投资场景，该场景使用从过滤后的高通胀制度数据中经自助重抽样得到的资产收益率。结果表明，LFNN策略在投资期末以超过90%的概率超越基准，其年化中位数回报率始终比被动基准策略高出约200个基点。