arXiv research

Paper proves large deviation principle for stochastic approximations.

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

We establish large deviation principles for convolutional neural networks.

Study large deviations in random walks on Lie groups.

Large deviation principles for multivariate stochastic volatility models.

Large deviation principle for deep neural networks with ReLU activation.

Random walks on hyperbolic spaces follow predictable large deviation principles.

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…

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…

Study large deviations in life insurance portfolios without identical distributions.

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

Study on implied volatility of an affine jump-diffusion model.

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

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

Unified approach to stochastic Volterra systems' deviations.

Large deviations theory applied to policy gradient methods.

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

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 …

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…

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

We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We consider three main applications: Conditional Gibbs measures on compact spaces, …

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…

This work accelerates constrained sampling using large deviation principles.

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

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

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 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 …

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

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…

In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the implied volatility. In addition, we prove that if the volatility function in an uncor…

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

Method generates plausible financial stress scenarios using large deviations.

Optimal insurance strategy for maximizing RDEU under various premium principles.

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

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…

Study provides LDP for non self-similar stochastic volatility models.

LIIT uses large deviations to train neural networks faster.

This work finds mixed equilibria in zero-sum games using interacting particle dynamics.

Study optimal offline RL with uncertainty sets and distribution shifts.

The paper explores optimal insurance contracts using various deviation measures.

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

This work extends the variance reduction method for the pricing of possibly path-dependent derivatives, which was developed in (Genin and Tankov, 2016) for exponential Lévy models, to affine stochastic volatility models (Keller-Ressel, 2011). We begin by proving a pathwise large deviations principle for affine stochast…

This paper optimizes importance sampling for rare-event options pricing under the Heston model.

In the present paper and the companion paper [9] a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on a complex algebraic varieties X is introduced, by sampling "temperature deformed" determinantal point processes. The main new ingredient is a large deviation principle for Gibbs…

Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distribut…

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