arXiv research

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

Paper proves large deviation principle for stochastic approximations.

Study large deviations in life insurance portfolios without identical distributions.

Study large deviations in random walks on Lie groups.

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.

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…

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…

We establish large deviation principles for convolutional neural networks.

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…

Large deviation principles for multivariate stochastic volatility models.

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

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

Study large deviations rates for SGD with strongly convex functions.

Random walks on hyperbolic spaces follow predictable large deviation principles.

We study utility indifference prices and optimal purchasing quantities for a non-traded contingent claim in an incomplete semi-martingale market with vanishing hedging errors. We make connections with the theory of large deviations. We concentrate on sequences of semi-complete markets where in the $n^{th}$ market, the …

The paper uses machine learning to compute rare event probabilities in stochastic systems.

We prove quantitative recurrence and large deviations results for the Teichmuller geodesci flow on a connected component of a stratum of the moduli space $Q_g$ of holomorphic unit-area quadratic differentials on a compact genus $g \geq 2$ surface.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

We study the small-time behaviour of the rough Bergomi model, introduced by Bayer, Friz and Gatheral (2016), and prove a large deviations principle for a rescaled version of the normalised log stock price process, which then allows us to characterise the small-time behaviour of the implied volatility.

Study on error probabilities of machine learning classification techniques using large deviations theory.

Sharp large deviations and Gibbs conditioning for portfolio credit risk models.

Method generates plausible financial stress scenarios using large deviations.

This work accelerates constrained sampling using large deviation principles.

LIIT uses large deviations to train neural networks faster.

We prove a large deviations principle for the class of multidimensional affine stochastic volatility models considered in (Gourieroux, C. and Sufana, R., J. Bus. Econ. Stat., 28(3), 2010), where the volatility matrix is modelled by a Wishart process. This class extends the very popular Heston model to the multivariate …

The paper studies large deviation principles for stochastic volatility models with reflection, focusing on binary barrier options and call prices.

Study large deviation in stationarized fully lifted blirp interpolation.

Sharp concentration results for sums of heavy-tailed random variables.

Improved adaptive algorithms for identifying the best arm in MABs with fixed budget.

We prove the first mathematical result relating the Yang-Mills measure on a compact surface and the Yang-Mills energy. We show that, at the small volume limit, the Yang-Mills measures satisfy a large deviation principle with a rate function which is expressed in a simple and natural way in terms of the Yang-Mills energ…

Bayesian neural networks explore rare fluctuations for better feature learning.

New theorem connects probabilistic permanental point processes to Monge-Ampère equation.

Study finds a small correction to Asian option volatility.

Sharp concentration bounds for i.i.d. variables.

We use the theory of large deviations to study the pricing of investment-grade tranches of synthetic CDO's. In this paper, we consider a heterogeneous pool of names. Our main tool is a large-deviations analysis which allows us to precisely study the behavior of a large amount of idiosyncratic randomness. Our calculatio…

We obtain a large deviation function for the stationary measures of twisted Brownian motions associated to the Lagrangians $L_λ(p,v)=\frac{1}{2}g_{p}(v,v)- λω_{p}(v)$, where $g$ is a $C^{\infty}$ Riemannian metric in a compact surface $(M,g)$ with nonpositive curvature, $ω$ is a closed 1-form such that the Aubry-Mather…

Due to their heterogeneity, insurance risks can be properly described as a mixture of different fixed models, where the weights assigned to each model may be estimated empirically from a sample of available data. If a risk measure is evaluated on the estimated mixture instead of the (unknown) true one, then it is impor…

Extends pricing methods for index options under rough volatility.

We study large deviations and rare default clustering events in a dynamic large heterogeneous portfolio of interconnected components. Defaults come as Poisson events and the default intensities of the different components in the system interact through the empirical default rate and via systematic effects that are comm…

We generalize classical large deviations theorems to the setting of complete Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using visocity solutions for Hamilton-Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The ap…

New method uses Coulomb gases for Monte Carlo integration with reduced errors.

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…

We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we study the structure of losses in a pool consisting of a continuum of types. We derive the corresponding rate function and show that it has …