arXiv research

Paper proves large deviation principle for stochastic approximations.

Large deviations theory applied to policy gradient methods.

Paper proposes a simple estimator for DPP correlation kernels.

Study finds a small correction to Asian option volatility.

Study large deviations in life insurance portfolios without identical distributions.

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

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.

Study large deviations in random walks on Lie groups.

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

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…

Study examines large deviations in random walks on hyperbolic spaces.

Paper explores SVGD for Bayesian inference, linking deterministic and stochastic dynamics.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

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…

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

Unified approach to stochastic Volterra systems' deviations.

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…

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 provide a direct proof of Cramér's theorem for geodesic random walks in a complete Riemannian manifold $(M,g)$. We show how to exploit the vector space structure of the tangent spaces to study large deviation properties of geodesic random walks in $M$. Furthermore, we reveal the geometric obstructions one runs into …

Large deviation principle for deep neural networks with ReLU activation.

We establish large deviation principles for convolutional neural networks.

Large deviation principles for multivariate stochastic volatility models.

The study analyzes how machine learning classifiers' error rates decrease exponentially based on large deviations theory.

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…

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

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

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

Proposes new deviation measures using Minkowski gauges.

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…

Realized statistics based on high frequency returns have become very popular in financial economics. In recent years, different non-parametric estimators of the variation of a log-price process have appeared. These were developed by many authors and were motivated by the existence of complete records of price data. Amo…

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 …

Study large deviations rates for SGD with strongly convex functions.

Random walks on hyperbolic spaces follow predictable large deviation principles.

Paper proposes a novel method to improve matrix completion with median loss for large datasets.

Analytical approximations for Asian option sensitivities in Black-Scholes model.

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…

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.

The paper develops bounds for predictive values in binary classification.

Study high-dimensional Bayesian linear regression using variational inference.

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

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…

Method generates plausible financial stress scenarios using large deviations.

Paper optimizes change-point detection using learned distributions from training sequences.

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 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 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.