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Predictive models often reinforce biases which were originally embedded in their training data, through skewed decisions. In such cases, mitigation methods are critical to ensure that, regardless of the prevailing disparities, model…
Motivated by amplitude calculations in string theory we establish basic properties of homotopy invariant iterated integrals on affine curves.
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
The LIBOR rate is currently scheduled for discontinuation, and the replacement advocated by regulators in the US is the Secured Overnight Financing Rate (SOFR). The change has the potential to disrupt the $200 trillion market of derivatives…
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…
In this short note, using our geometric method introduced in a previous paper \cite{phl} and initiated by \cite{ave}, we derive an asymptotic swaption implied volatility at the first-order for a general stochastic volatility Libor Market…
We price European-style options written on forward contracts in a commodity market, which we model with an infinite-dimensional Heath-Jarrow-Morton (HJM) approach. For this purpose we introduce a new class of state-dependent volatility…
We propose a new model for the level I of a Limit Order Book (LOB), which incorporates the information about the standing orders at the opposite side of the book after each price change and the arrivals of new orders within the spread. Our…
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong…
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess…
We construct a no-arbitrage model of bond prices where the long bond is used as a numeraire. We develop bond prices and their dynamics without developing any model for the spot rate or forward rates. The model is arbitrage free and all…
This article proposes a calibration framework for complex option pricing models that jointly fits market option prices and the term structure of variance. Calibrated models under the conventional objective function, the sum of squared…
Recent literature has seen a significant focus on building machine learning models with specific properties such as fairness, i.e., being non-biased with respect to a given set of attributes, calibration i.e., model confidence being aligned…
We consider the computation of model-free bounds for multi-asset options in a setting that combines dependence uncertainty with additional information on the dependence structure. More specifically, we consider the setting where the…
Machine learning (ML) models are increasingly used for high-stake applications that can greatly impact people's lives. Despite their use, these models have the potential to be biased towards certain social groups on the basis of race,…
We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
This paper constructs and studies the long-term factorization of affine pricing kernels into discounting at the rate of return on the long bond and the martingale component that accomplishes the change of probability measure to the long…
As the frontiers of applied statistics progress through increasingly complex experiments we must exploit increasingly sophisticated inferential models to analyze the observations we make. In order to avoid misleading or outright erroneous…
An important task in the field of sensor technology is the efficient implementation of adaptation procedures of measurements from one sensor to another sensor of identical design. One idea is to use the estimation of an affine…