Design of Neuro-Stochastic Bayesian Networks for Nonlinear Chaotic Differential Systems in Financial Mathematics

The research community’s treatise on computational economics and financial models has promising interest for the exploration and exploitation of artificial intelligence (AI)-based computing paradigm to offer enriched efficacies for business stratagems, consumer utility, and scarce resource management for enriched society evolution. In this study, AI-based neuro-stochastic Bayesian networks (NSBNs) are presented for mathematical models that govern the dynamics of nonlinear chaotic financial differential systems (NCFDSs). The descriptive expressions for NCFDS are portrayed through multi-class differential compartments for macroeconomic agents in terms of interest rate, investment demand, and price index. The reference data acquisition for the execution of the multi-layer structure of NSBNs is performed with Adams numerical procedure for sundry scenarios of NCFDSs by varying the cost per investment, saving amount, as well as, commercial market demand elasticity. The designed NSBN outcomes consistently overlap with the reference solutions having negligible magnitude of error for each scenario of NCFDS. The efficacy of proposed NSBNs is presented through mean square error based convergence curves, illustrations for adaptive controlling parameters, 2D–3D visual depictions, error histogram studies, and regression indices for variants of nonlinear chaotic differential systems in mathematical finance.