Neural Functionally Generated Portfolios

Abstract: We introduce a novel neural-network-based approach to learning the generating function $G(\cdot)$ of a functionally generated portfolio (FGP) from synthetic or real market data. In the neural network setting, the generating function is represented as $G_{\theta}(\cdot)$, where $\theta$ is an iterable neural network parameter vector, and $G_{\theta}(\cdot)$ is trained to maximise investment return relative to the market portfolio. We compare the performance of the Neural FGP approach against classical FGP benchmarks. FGPs provide a robust alternative to classical portfolio optimisation by bypassing the need to estimate drifts or covariances. The neural FGP framework extends this by introducing flexibility in the design of the generating function, enabling it to learn from market dynamics while preserving self-financing and pathwise decomposition properties.