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This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other…
Conditioning is crucial in applied science when inference involving time series is involved. Belief calculus is an effective way of handling such inference in the presence of epistemic uncertainty -- unfortunately, different approaches to…
A time-dependent product is introduced between the observables of a dissipative quantum system, that accounts for the effects of dissipation on observables and commutators. In the $t \to \infty$ limit this yields a contracted algebra. The…
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…
In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly…
Large language models are reshaping quantitative investing by turning unstructured financial information into evidence-grounded signals and executable decisions. This survey synthesizes research with a focus on equity return prediction and…
We present a new framework for modeling the statistical behavior of both fully developed turbulence and short-term dynamics of financial markets based on the nonextensive thermostatistics proposed by Tsallis. We also show that intermittency…
Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price velocity and price acceleration, we construct a general classification of the possible patterns characterizing the…
Financial networks have become extremely useful in characterizing the structure of complex financial systems. Meanwhile, the time evolution property of the stock markets can be described by temporal networks. We utilize the temporal network…
Conventional embedding-based models approach event time prediction in temporal knowledge graphs (TKGs) as a ranking problem. However, they often fall short in capturing essential temporal relationships such as order and distance. In this…
Predicting volatility in financial markets, including stocks, index ETFs, foreign exchange, and cryptocurrencies, remains a challenging task due to the inherent complexity and non-linear dynamics of these time series. In this study, I apply…
We study a new measure of codependency in the second moment of a continuous-time multivariate asset price process, which we name the realized copula of volatility. The statistic is based on local volatility estimates constructed from…
We consider the scenario where the parameters of a probabilistic model are expected to vary over time. We construct a novel prior distribution that promotes sparsity and adapts the strength of correlation between parameters at successive…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
An extension of the idea of state tameness is presented in a dynamic framework. The proposed model for financial markets is rich enough to provide analytical tools that are mostly obtained in models that arise as the solution of SDEs with…
Quantitative structuring is a rigorous framework for the design of financial products. We show how it incorporates traditional investment ideas while supporting a more accurate expression of clients' views. We touch upon adjacent topics…
Financial institutions and insurance companies that analyze the evolution and sources of profits and losses often look at risk factors only at discrete reporting dates, ignoring the detailed paths. Continuous-time decompositions avoid this…
Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading,…
This paper develops a comprehensive theoretical framework that imports concepts from stochastic thermodynamics to model price impact and characterize the feasibility of round-trip arbitrage in financial markets. A trading cycle is treated…
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…