arXiv research

This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the numéraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the…

We develop the fundamental theorem of asset pricing in a probability-free infinite-dimensional setup. We replace the usual assumption of a prior probability by a certain continuity property in the state variable. Probabilities enter then endogenously as full support martingale measures (instead of equivalent martingale…

Unified framework models multiple financial and insurance term structures.

The paper studies market viability and completeness in discrete markets.

Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.

In a semimartingale financial market model, it is shown that there is equivalence between absence of arbitrage of the first kind (a weak viability condition) and the existence of a strictly positive process that acts as a local martingale deflator on nonnegative wealth processes.

We undertake a study of markets from the perspective of a financial agent with limited access to information. The set of wealth processes available to the agent is structured with reasonable economic properties, instead of the usual practice of taking it to consist of stochastic integrals against a semimartingale integ…

Optimizes functionals on probability space using ICNNs.

Blockchain markets with paid-priority trading can lead to biased prices and reduced liquidity.

Bayesian Optimization tackles hidden constraints in architecture optimization.

We consider a general class of diffusion-based models and show that, even in the absence of an Equivalent Local Martingale Measure, the financial market may still be viable, in the sense that strong forms of arbitrage are excluded and portfolio optimisation problems can be meaningfully solved. Relying partly on the rec…

New method makes machine learning approximations unbiased and efficient.

Transductive Adversarial Networks (TAN) is a novel domain-adaptation machine learning framework that is designed for learning a conditional probability distribution on unlabelled input data in a target domain, while also only having access to: (1) easily obtained labelled data from a related source domain, which may ha…

Study on cyber insurance viability using statistical models.

This short note aims to point out mistakes in one of the implications for Theorem 2.8 in Bayraktar and Yu [Mathematical Finance, 28 (2018), pp. 800-838], which weakens the statement of this theorem.

We consider a financial market model with a single risky asset whose price process evolves according to a general jump-diffusion with locally bounded coefficients and where market participants have only access to a partial information flow. For any utility function, we prove that the partial information financial marke…

The paper uses stochastic control to analyze interest rate markets with roll-over risk.

Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences b…

Study arbitrage in financial markets with trading restrictions.

Inverse classification uses an induced classifier as a queryable oracle to guide test instances towards a preferred posterior class label. The result produced from the process is a set of instance-specific feature perturbations, or recommendations, that optimally improve the probability of the class label. In this work…

We develop a new approach to solving classification problems, which is bases on the theory of coherent measures of risk and risk sharing ideas. The proposed approach aims at designing a risk-averse classifier. The new approach allows for associating distinct risk functional to each classes. The risk may be measured by …

Random Function Descent improves optimization in high dimensions.

We consider the problem of function approximation by two-layer neural nets with random weights that are "nearly Gaussian" in the sense of Kullback-Leibler divergence. Our setting is the mean-field limit, where the finite population of neurons in the hidden layer is replaced by a continuous ensemble. We show that the pr…

Study liquidity provision in decentralized exchanges considering risk aversion and replication costs.

The Dybvig-Ingersoll-Ross (DIR) theorem states that, in arbitrage-free term structure models, long-term yields and forward rates can never fall. We present a refined version of the DIR theorem, where we identify the reciprocal of the maturity date as the maximal order that long-term rates at earlier dates can dominate …

We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizi…

Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that …

Entropic herding generates smooth distributions for probabilistic modeling.

A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption, namely, absence of arbitrages of t…

Our paper introduces an efficient combination of established techniques to improve classifier performance, in terms of accuracy and training time. We achieve two-fold to ten-fold speedup in nearing state of the art accuracy, over different model architectures, by dynamically tuning the learning rate. We find it especia…

Study deep neural nets for solving complex insurance equations.

In the landscape of TD algorithms, the Q($σ$, $λ$) algorithm is an algorithm with the ability to perform a multistep backup in an online manner while also successfully unifying the concepts of sampling with using the expectation across all actions for a state. $σ\in [0, 1]$ indicates the extent to which sampling is use…

New method for pricing and hedging options in risky markets.

We study arbitrage opportunities, market viability and utility maximization in market models with an insider. Assuming that an economic agent possesses from the beginning an additional information in the form of a random variable G, which only becomes known to the ordinary agents at date T, we give criteria for the No …

Develops MIS, a probabilistic model for multi-industry classification.

Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up artificial neural networks architecture selection. In this work, we propose an improved…

When working with three-dimensional data, choice of representation is key. We explore voxel-based models, and present evidence for the viability of voxellated representations in applications including shape modeling and object classification. Our key contributions are methods for training voxel-based variational autoen…

RL research overhypes potential but lacks deployable solutions.

New method solves complex optimization problems with real-time learning.

We propose a novel neural network embedding approach to model power transmission grids, in which high voltage lines are disconnected and reconnected with one-another from time to time, either accidentally or willfully. We call our architeture LEAP net, for Latent Encoding of Atypical Perturbation. Our method implements…

Recent research showed that deep neural networks are highly sensitive to so-called adversarial perturbations, which are tiny perturbations of the input data purposely designed to fool a machine learning classifier. Most classification models, including deep learning models, are highly vulnerable to adversarial attacks.…

Deep neural networks reduce portfolio tail-risk by 99% in crisis-era simulations.

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its development. In doing so, we demonstrate the viability of hyperbolic geometry f…

Bayesian networks and ML improve COVID-19 symptom classification and severity analysis.

Automation of machine learning model development is increasingly becoming an established research area. While automated model selection and automated data pre-processing have been studied in depth, there is, however, a gap concerning automated model adaptation strategies when multiple strategies are available. Manually…

Online portfolio selection research has so far focused mainly on minimizing regret defined in terms of wealth growth. Practical financial decision making, however, is deeply concerned with both wealth and risk. We consider online learning of portfolios of stocks whose prices are governed by arbitrary (unknown) stationa…

Systematic reviews, which summarize and synthesize all the current research in a specific topic, are a crucial component to academia. They are especially important in the biomedical and health sciences, where they synthesize the state of medical evidence and conclude the best course of action for various diseases, path…

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admiss…