arXiv research

Introduces Star-Shaped deviation measures for risk analysis.

Paper characterizes monotonic mean-deviation risk measures.

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the Gärtner-Ellis theorem and sharp large deviations tools.

Paper proves large deviation principle for stochastic approximations.

In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a generalised conditional variance formula. We show that, under a domination condition,…

Study large deviations in life insurance portfolios without identical distributions.

Study large deviations for hypoelliptic diffusion on sub-Riemannian manifolds.

Proposes new deviation measures using Minkowski gauges.

In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law invariant and recursive is the variance. We also solve the problem of optimal risk-sha…

We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised vari…

Importance sampling has become an important tool for the computation of tail-based risk measures. Since such quantities are often determined mainly by rare events standard Monte Carlo can be inefficient and importance sampling provides a way to speed up computations. This paper considers moderate deviations for the wei…

Connections between Lie derivatives and the deviation equation has been investigated in spaces with affine connection. The deviation equations of the geodesics as well as deviation equations of non-geodesics trajectories have been obtained on this base. This is done via imposing certain conditions on the Lie derivative…

Unified approach to stochastic Volterra systems' deviations.

Study large deviations in random walks on Lie groups.

Deviation inequalities and limit laws for random walks on metric spaces.

Let $M$ be a smooth manifold and $\mathcal{S}$ a semi-spray defined on a sub-bundle $\mathcal{C}$ of the tangent bundle $TM$. In this work it is proved that the only non-trivial $k$-jet approximation to the exact geodesic deviation equation of $\mathcal{S}$, linear on the deviation functions and invariant under an spec…

Optimizes variance reduction in Heston model using large and moderate deviations.

Large deviations theory applied to policy gradient methods.

Study examines large deviations in random walks on hyperbolic spaces.

Study large deviations and speed of random walks in hyperbolic spaces.

Deviation inequalities for stochastic approximation methods.

Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated on a single variable. The regime of large deviations is separated from the regi…

We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with random slipping and twisting. The system is modelled by a stochastic differential equation of Stratonovich-type driven by semimartingales, on…

Researchers introduce a method to assess the safety of interpretable machine learning models.

The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between arbitrary, geodesic or not, paths) in such spaces are investigated.

Large deviation principle for deep neural networks with ReLU activation.

Study large deviations in fractional volatility models with non-Gaussian volatility.

In these notes, we present some methods and applications of large deviations to finance and insurance. We begin with the classical ruin problem related to the Cramer's theorem and give en extension to an insurance model with investment in stock market. We then describe how large deviation approximation and importance s…

The paper explores optimal insurance contracts using various deviation measures.

We establish large deviation principles for convolutional neural networks.

Paper proposes a new daily benchmark for post-GFC government bond CIP deviations.

The paper establishes a connection between different risk measures and their risk contributions.

Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret…

The paper analyzes how a known density function can be deviated by a mixture distribution as more data is collected.

Large deviation principles for multivariate stochastic volatility models.

Classifiers trained with class-imbalanced data are known to perform poorly on test data of the "minor" classes, of which we have insufficient training data. In this paper, we investigate learning a ConvNet classifier under such a scenario. We found that a ConvNet significantly over-fits the minor classes, which is quit…

Novel concentration inequalities are obtained for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We derive distribution-free deviation bounds with sublinear exponents in deviation size for missing mass and improve the results of Berend and Kontorovich (2013) and Yari Saeed…

Optimal insurance strategy for maximizing RDEU under various premium principles.

Study volatility models with rough paths, focusing on large deviations and option behavior.

Objective: A median of 14.4% of patient undergone at least one adverse event during surgery and a third of them are preventable. The occurrence of adverse events forces surgeons to implement corrective strategies and, thus, deviate from the standard surgical process. Therefore, it is clear that the automatic identifica…

In a coordinate free form are found the (deviation) equations satisfied by the (infinitesimal) deviation vector, relative velocity, relative momentum, relative acceleration and relative energy of two point particles in a differentiable manifold the tangent bundle of which is endowed with a linear transport along paths,…

Anomaly detection for high-dimensional data using large deviations principle.

Paper analyzes and accelerates Langevin Monte Carlo methods using large deviations theory.

Optimal learning via moderate deviations theory improves statistical accuracy.

Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appro…

A new method to break down insurance costs into risk and uncertainty.

We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those surfaces arising from rational polygonal billiards.

Optimal payoff choice constrained by Bregman-Wasserstein divergence.