Parameter estimation of uncertain differential equation by implementing an optimized artificial neural network

Abstract

This study suggests a novel method for estimation of uncertain stock model parameters driven by Liu process. The proposed method decomposes the parameter estimation problem into two sub-problems: the first sub-problem implements an optimized artificial neural network based on the observed data, and the next sub-problem estimates the uncertain model parameters according to the optimized artificial neural network. We apply Nelder–Mead algorithm to optimize the artificial neural network and parameter estimation problem. The main supremacy of the presented method is that the estimation problem is independent of time intervals among observations and can be used to model future data. Providing a comparative method shows that the proposed approach can be effective for non-linear problems in which the artificial neural network structures perform well.