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Data is vital in enabling machine learning models to advance research and practical applications in finance, where accurate and robust models are essential for investment and trading decision-making. However, real-world data is limited…
Hierarchical autocorrelation in the error term of linear models arises when sampling units are related to each other according to a tree. The residual covariance is parametrized using the tree-distance between sampling units. When…
The Ornstein-Uhlenbeck (OU) process plays a major role in the analysis of the evolution of phenotypic traits along phylogenies. The standard OU process includes drift and stabilizing selection and assumes that species evolve independently.…
We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We…
We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the…
This paper presents a numerical model to solve the problem of cash accumulation strategies for products with an unknown future price, like assets. Stock prices are modeled by a discretized Wiener Process, and by the means of ordinary…
In this paper we develop a framework for estimating Probability of Default (PD) based on stochastic models governing an appropriate asset value processes. In particular, we build upon a L\'evy-driven Ornstein-Uhlenbeck process and consider…
We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process…
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…
Machine learning algorithms dedicated to financial time series forecasting have gained a lot of interest. But choosing between several algorithms can be challenging, as their estimation accuracy may be unstable over time. Online aggregation…
In usual stochastic volatility models, the process driving the volatility of the asset price evolves according to an autonomous one-dimensional stochastic differential equation. We assume that the coefficients of this equation are smooth.…
We introduce an ensemble learning method based on Gaussian Process Regression (GPR) for predicting conditional expected stock returns given stock-level and macro-economic information. Our ensemble learning approach significantly reduces the…
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[…
The price movement prediction of stock market has been a classical yet challenging problem, with the attention of both economists and computer scientists. In recent years, graph neural network has significantly improved the prediction…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
The intricate behavior patterns of financial markets are influenced by fundamental, technical, and psychological factors. During times of high volatility and regime shifts causes many traditional strategies like trend-following or…
There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
Stock exchanges are considered major players in financial sectors of many countries. Most Stockbrokers, who execute stock trade, use technical, fundamental or time series analysis in trying to predict stock prices, so as to advise clients.…
Assuming frictionless trading, classical stochastic portfolio theory (SPT) provides relative arbitrage strategies. However, the costs associated with real-world execution are state-dependent, volatile, and under increasing stress during…