A kernel-based control approach for multi-period assets allocation based on lower partial moments

In quantitative finance, multi-period portfolio optimization can be reformulated as a stochastic optimal control problem, and standard feedback tools can be employed for its analysis. The performance of the trading solutions strongly depend on the quality of the model of the returns. Therefore, data-driven solutions have been recently proposed to optimize simple-linear allocation policies, based only on a set of possible market scenarios. In this work, kernel-based methods are proposed to design more complex and effective control actions, providing better trade-offs in terms of risk and investment performance with respect to linear ones, by preserving convexity. The proposed approach relies on the minimization of the Lower Partial Moments (LPM) risk measure. The effectiveness of the method is shown on a set of real historical financial data.