Machine learning, neural networks

Dynamic neural network implementation of the Heston model

G. I. Belyavskiy^a, M. A. Butakova^b, N. V. Danilova^a, V. V. Makhno<sup>a

a</sup> Southern Federal University, Rostov-on-Don, Russia
^b Scientific Research and Design Institute of Informatization, Automation and Communication of Railway Transport, Rostov-on-Don

Abstract: The relationship between a system of stochastic differential equations and a neural network is studied using the example of the Heston model, which is relevant in stochastic financial mathematics. More specifically, the neural network was used to solve the problem of hidden of one of the components of the phase vector of a stochastic dynamic system described by a system of stochastic differential equations. The solution is based on the combination of signal filtering theory and methods for solving partial differential equations using a neural network. The synthesized neural network solves the problem of calculating a dynamic investment strategy that minimizes investment risk based on a random process of cost evolution. The results obtained are transferred to the network solution of other stochastic control problems based on an incompletely observed phase vector.

Keywords: neural network, deep learning, Heston model, partial differential equations, signal filtering.

DOI: 10.14357/20718594250407

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