Probabilistic fuzzy neural networks and interval arithmetic techniques for forecasting equities
Document Type
Article
Publication Title
Probabilistic fuzzy neural networks and interval arithmetic techniques for forecasting equities
Abstract
We develop an architecture for a neural network specifically for forecasting equities. By implementing the already successful probabilistic fuzzy neural network (PFNN) (developed by Han-Xiong Li and Zhi Liu), we are able to handle complex stochastic uncertainties. In light of the Black Scholes Merton model, we use triangular fuzzy numbers in its calculation to include the range instead of a spot price for an investment. Stock market forecasting is multi-dimensional, where time is not the only variable of interest and is non-linear. However, the stochastic gradient descent accounts for optimization in one-dimension for a convex function. We optimize the family of functions with the Hamilton-Jacobi partial differential equation to more accurately represent a non-linear and non-convex function (developed by Chaudhari et al.). In this approach, we will observe the neural network in light of the Dupire formula. Dupire continues the Black Scholes Merton model (BSM), but addresses the weakness of the volatility in the model. By observing volatility as a function of time, Dupire removes the predictable volatility smile found in the BSM model. We optimize this volatility to minimize the risk in forecasting for an optimal prediction. In a future study, we plan to analyze the program’s efficiency for forecasting stock options.
DOI
https://doi.org/10.1007/978-3-030-40814-5_13
Publication Date
Spring 3-25-2020
Recommended Citation
Gauff, A., Munoz Barona, H. (2020). Probabilistic Fuzzy Neural Networks and Interval Arithmetic Techniques for Forecasting Equities. In: Ceberio, M., Kreinovich, V. (eds) Decision Making under Constraints. Studies in Systems, Decision and Control, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-030-40814-5_13