We introduce a novel multivariate GARCH model with flexible convolution-t distributions that is applicable in high-dimensional systems. The model is called Cluster GARCH because it can accommodate cluster structures in the conditional correlation matrix and in the tail dependencies. The expressions
We investigate propagation of convexity and convex ordering on a typical discrete-time stochastic optimal control problem, namely the pricing of swing option. The dynamics of the underlying asset is modelled by the Euler scheme of a Brownian diffusion with affine drift, and convex volatility. We pro
We study the mean field limit of a rank-based model with common noise, which arises as an extension to models for the market capitalization of firms in stochastic portfolio theory. We show that, under certain conditions on the drift and diffusion coefficients, the empirical cumulative distribution f
This study aims to examine the intricate dynamics between BRICS traditional stock assets and the evolving landscape of cryptocurrencies. Using a time-varying parameter vector autoregression model (TVP-VAR), we have analyzed data from the BRICS stock market index, cryptocurrencies, and indicators fro
The scope of this manuscript is to review some recent developments in statistics for discretely observed semimartingales which are motivated by applications for financial markets. Our journey through this area stops to take closer looks at a few selected topics discussing recent literature. We moreo
The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was fir
\begin{“abstract”} In this paper, we integrated the statistical arbitrage strategy, pairs trading, into the Black-Litterman model and constructed efficient mean-variance portfolios. Typically, pairs trading underperforms under volatile or distressed market condition because the selected asset pairs
Trend following and momentum investing are common strategies employed by asset managers. Even though they can be helpful in the proper situations, they are limited in the sense that they work just by looking at past, as if we were driving with our focus on the rearview mirror. In this paper, we advo
To comply with increasingly stringent international standards in risk management and regulation, several approaches have been developed in the literature for forecasting tail-risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). However, the accuracy of these measures can be signifi
The gas fee, paid for inclusion in the blockchain, is analyzed in two parts. First, we consider how effort in terms of resources required to process and store a transaction turns into a gas limit, which, through a fee, comprised of the base and priority fee in the current version of Ethereum, is con
An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders’ belief and risk aversion. This paper proposes a trading strategy model in the optimal Merton framework that is representative of the collective beh
In this work we address the question of the Multifractal detrended cross-correlation analysis method that has been subject to some controversies since its inception almost two decades ago. To this end we propose several new options to deal with negative cross-covariance among two time series, that m
There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to gener
Building on the macroscopic market making framework as a control problem, this paper investigates its extension to stochastic games. In the context of price competition, each agent is benchmarked against the best quote offered by the others. We begin with the linear case. While constructing the solu
Introducing an algebraic framework for modeling limit order books (LOBs) with tools from physics and stochastic processes, our proposed framework captures the creation and annihilation of orders, order matching, and the time evolution of the LOB state. It also enables compositional settings, accommo
The European carbon market plays a pivotal role in the European Union’s ambitious target of achieving carbon neutrality by 2050. Understanding the intricacies of factors influencing European Union Emission Trading System (EU ETS) market prices is paramount for effective policy making and strategy im
We introduce and study geometric Bass martingales. Bass martingales were introduced in \cite{Ba83} and studied recently in a series of works, including \cite{BaBeHuKa20,BaBeScTs23}, where they appear as solutions to the martingale version of the Benamou-Brenier optimal transport formulation. These a
This paper concerns a continuous time mean-variance (MV) portfolio selection problem in a jump-diffusion financial model with no-shorting trading constraint. The problem is reduced to two subproblems: solving a stochastic linear-quadratic (LQ) control problem under control constraint, and finding a
The accurate prediction of stock movements is crucial for investment strategies. Stock prices are subject to the influence of various forms of information, including financial indicators, sentiment analysis, news documents, and relational structures. Predominant analytical approaches, however, tend
Detecting anomalies in general ledger data is of utmost importance to ensure trustworthiness of financial records. Financial audits increasingly rely on machine learning (ML) algorithms to identify irregular or potentially fraudulent journal entries, each characterized by a varying number of transac