Under the impact of both increasing credit pressure and low economic returns characterizing developed countries, investment levels have decreased over recent years. Moreover, the recent turbulence caused by the COVID-19 crisis has accelerated the latter process. Within this scenario, we consider the so-called Volatility Target (VolTarget) strategy. In particular, we focus our attention on estimating volatility levels of a risky asset to perform a VolTarget simulation over two different time horizons. We first consider a 20 year period, from January 2000 to January 2020, then we analyse the last 12 months to emphasize the effects related to the COVID-19 virus’s diffusion. We propose a hybrid algorithm based on the composition of a GARCH model with a Neural Network (NN) approach. Let us underline that, as an alternative to standard allocation methods based on realized and backward oriented volatilities, we exploited an innovative forward-looking estimation process exploiting a Machine Learning (ML) solution. Our solution provides a more accurate volatility estimation, allowing us to derive an effective investor risk-return profile during market crisis periods. Moreover, we show that, via a forward-looking VolTarget strategy while using an ML-based prediction as the input, the average outcome for an investment in a drawdown plan is more sustainable while representing an efficient risk-control solution for long time period investments.
We provide a rigorous mathematical formulation of Deep Learning (DL) methodologies through an in-depth analysis of the learning procedures characterizing Neural Network (NN) models within the theoretical frameworks of Stochastic Optimal Control (SOC) and Mean-Field Games (MFGs). In particular, we show how the supervised learning approach can be translated in terms of a (stochastic) mean-field optimal control problem by applying the Hamilton–Jacobi–Bellman (HJB) approach and the mean-field Pontryagin maximum principle. Our contribution sheds new light on a possible theoretical connection between mean-field problems and DL, melting heterogeneous approaches and reporting the state-of-the-art within such fields to show how the latter different perspectives can be indeed fruitfully unified.
In this paper we derive a unified perspective for Optimal Transport (OT) theory and Mean Field Control (MFC) theory to analyse the learning process for Neural Networks algorithms in a high-dimensional framework. We consider Mean Field Neural Networks in the context of MFC theory, specifically the mean field formulation of OT theory that allows the development of highly efficient algorithms while providing a powerful tool in the context of explainable Artificial Intelligence.
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