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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…

Modelling all possible life cycles of a company in a highly competitive economic environment gives a significant advantage to the owner in his business investment activities. This article proposes and analyses a dynamic model of a company's…

We investigate the financial market dynamics by introducing a heterogeneous agent-based opinion formation model. In this work, we organize the individuals in a financial market by their trading strategy, namely noise traders and…

We consider the following problem in stochastic portfolio theory. Are there portfolios that are relative arbitrages with respect to the market portfolio over very short periods of time under realistic assumptions? We answer a slightly…

We introduce the notion of performative power, which measures the ability of a firm operating an algorithmic system, such as a digital content recommendation platform, to cause change in a population of participants. We relate performative…

Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a…

Financial forecasting plays an important role in making informed decisions for financial stakeholders, specifically in the stock exchange market. In a traditional setting, investors commonly rely on the equity research department for…

Predictions in the social world generally influence the target of prediction, a phenomenon known as performativity. Self-fulfilling and self-negating predictions are examples of performativity. Of fundamental importance to economics,…

In this paper we explore the usage of deep reinforcement learning algorithms to automatically generate consistently profitable, robust, uncorrelated trading signals in any general financial market. In order to do this, we present a novel…

In this paper, we study the herding phenomena in financial markets arising from the combined effect of (1) non-coordinated collective interactions between the market players and (2) concurrent reactions of market players to dynamic market…

Choice modeling is at the core of understanding how changes to the competitive landscape affect consumer choices and reshape market equilibria. In this paper, we propose a fundamental characterization of choice functions that encompasses a…

Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…

A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…

We present a novel microscopic stock market model consisting of a large number of random agents modeling traders in a market. Each agent is characterized by a set of parameters that serve to make iterated predictions of two successive…

This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…

These notes give a summary of techniques used in large deviation theory to study the fluctuations of time-additive quantities, called dynamical observables, defined in the context of Langevin-type equations, which model equilibrium and…

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem…

Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were…

Performing effective preference-based data retrieval requires detailed and preferentially meaningful structurized information about the current user as well as the items under consideration. A common problem is that representations of items…

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of…