A Novel Modeling Technique for the Forecasting of Multiple-Asset Trading Volumes: Innovative Initial-Value-Problem Differential Equation Algorithms for Reinforcement Machine Learning

Liquidity risk arises from the inability to unwind or hedge trading positions at the prevailing market prices. The risk of liquidity is a wide and complex topic as it depends on several factors and causes. While much has been written on the subject, there exists no clear-cut mathematical description of the phenomena and typical market risk modeling methods fail to identify the effect of illiquidity risk. In this paper, we do not propose a definitive one either, but we attempt to derive novel mathematical algorithms for the dynamic modeling of trading volumes during the closeout period from the perspective of multiple-asset portfolio(s), as well as for financial entities with different subsidiary firms and multiple agents. The robust modeling techniques are based on the application of initial-value-problem differential equations technique for portfolio selection and risk management purposes. This paper provides some crucial parameters for the assessment of the trading volumes of multiple-asset portfolio(s) during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed-form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half-life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. The developed modeling algorithms are appealing in terms of theory and are promising for practical econophysics applications, particularly in developing dynamic and robust portfolio management algorithms in light of the 2007-2009 global financial crunch. In addition, they can be applied to artificial intelligence and machine learning for the policymaking process, reinforcement machine learning techniques for the Internet of Things (IoT) data analytics, expert systems in finance, FinTech, and within big data ecosystems.