  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.
