مقاله انگلیسی پیش بینی های مالی بلندمدت بر اساس انتگرال های مسیر فاینمن- دیراک
Abstract
Keywords
Financial path prediction using stochastic equations and the Feynman–Dirac path integral
Deep Bayesian neural network for predicting drift and the volatility
Generating financial trajectories with a temporal GAN
GAN architectures
Experimental results
Summary and conclusions
CRediT authorship contribution statement
Declaration of Competing Interest
Acknowledgement
References
Abstract
This paper presents a new deep learning framework, QuantumPath, for long-term stock price prediction, which is of great significance in portfolio management and risk mitigation, especially when the market becomes volatile due to unpredictable circumstances such as a pandemic. Our approach is based on stochastic equations, the Feynman–Dirac path integral, deep Bayesian networks, and temporal generative adversarial neural networks (tGAN). The expected financial trajectory is evaluated with a Feynman–Dirac path integral. The latter involves summing all possible financial trajectories that could have been taken by the financial instrument. These trajectories are generated with a t-GAN. A probability is attributed to each point of each path. The probability is a function of the Lagrangian, which is derived from a stochastic equation describing the temporal evolution of the stock. The drift and the volatility at each point, which are required in order to evaluate the Lagrangian, are predicted with a deep Bayesian neural network. Given that the evolution of a stock’s price is isomorphic to a time series, our temporal GAN consists of long short-term memory (LSTM) neural networks, which introduce a memory mechanism, and temporal convolutional neural networks (TCN), which ensure causality. Stock prices are predicted over periods of twenty and thirty days for nine stocks, eight of which are included in the S&P 500 index. Our experimental results clearly demonstrate the efficiency of our approach.
The stock market is known for its erratic behaviour (Ziemba et al., 2017) with a 2020 episode resulting from the pandemic (Zhang et al., 2020; Ashraf, 2020). During the first quarter of 2020, while numerous companies experienced a sharp decline in their value, others such as Amazon, Walmart, and Tesla were sharply rising. As a result, those who invested in these companies prior to the pandemic made substantial profits while others suffered heavy losses (Nicola et al., 2020). In such contexts, stock price prediction may contribute to improving the return on investment while also mitigating the risks associated with uncertainty (Zhou et al., 2018). Generative models have the ability to learn the probability density function associated with a dataset (e.g., audio and images) (Lucic et al., 2018) while the posterior distribution may be inferred from discriminative models (Ulusoy & Bishop, 2006). Generative adversarial networks (GAN) are generative models that were first introduced by (Goodfellow et al., 2014). They aim to generate synthetic data with the same probability distribution function as the training dataset. They consist of a generator that produces synthetic data and a discriminator, which evaluates the discrepancy between the synthetic data and the real data.