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Stock market forecasting is a classic problem that has been thoroughly investigated using machine learning and artificial neural network based tools and techniques. Interesting aspects of this problem include its time reliance as well as…
Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here we model the price…
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downfalls, including the occurrence of arbitrage when implemented…
Stock price prediction is challenging due to global economic instability, high volatility, and the complexity of financial markets. Hence, this study compared several machine learning algorithms for stock market prediction and further…
We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is…
Parametric estimation of stochastic differential equations (SDEs) has been a subject of intense studies already for several decades. The Heston model for instance is driven by two coupled SDEs and is often used in financial mathematics for…
This paper contributes a new machine learning solution for stock movement prediction, which aims to predict whether the price of a stock will be up or down in the near future. The key novelty is that we propose to employ adversarial…
The prediction of a stock market direction may serve as an early recommendation system for short-term investors and as an early financial distress warning system for long-term shareholders. Many stock prediction studies focus on using…
This study investigates the application of machine learning techniques, specifically Neural Networks, Random Forests, and CatBoost for option pricing, in comparison to traditional models such as Black-Scholes and Heston Model. Using both…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
In the previous paper (Inverse Problems, 32, 015010, 2016), a new heuristic mathematical model was proposed for accurate forecasting of prices of stock options for 1-2 trading days ahead of the present one. This new technique uses the…
In this project, we propose to explore the Kalman filter's performance for estimating asset prices. We begin by introducing a stochastic mean-reverting processes, the Ornstein-Uhlenbeck (OU) model. After this we discuss the Kalman filter in…
This paper develops a model for the bid and ask prices of a European type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend…
In this paper, we consider the drawdown and drawup of the fractional Brownian motion with trend, which corresponds to the logarithm of geometric fractional Brownian motion representing the stock price in financial market. We derive the…
Classical technical analysis methods of stock evolution are recalled, i.e. the notion of moving averages and momentum indicators. The moving averages lead to define death and gold crosses, resistance and support lines. Momentum indicators…
We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The…
This paper tries to address the problem of stock market prediction leveraging artificial intelligence (AI) strategies. The stock market prediction can be modeled based on two principal analyses called technical and fundamental. In the…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
This work considers a stochastic model in which the uncertainty is driven by a multidimensional Brownian motion. The market price of risk process makes the transition between real world probability measure and risk neutral probability…
Predicting future direction of stock markets using the historical data has been a fundamental component in financial forecasting. This historical data contains the information of a stock in each specific time span, such as the opening,…