arXiv research

Introduces Star-Shaped deviation measures for risk analysis.

Paper characterizes monotonic mean-deviation risk measures.

The paper explores optimal insurance contracts using various deviation measures.

Proposes new deviation measures using Minkowski gauges.

Study large deviations rates for SGD with strongly convex functions.

Optimal payoff choice constrained by Bregman-Wasserstein divergence.

Large deviations theory applied to policy gradient methods.

Simple conditions for comonotonic additive risk measures from acceptance sets.

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

Optimal learning via moderate deviations theory improves statistical accuracy.

We review the dynamics of the returns of Leveraged Exchange Traded Funds (LETFs) and propose a new measure of realized volatility: Shortfall from Maximum Convexity. We show that SMC has a more intuitive interpretation and provides more statistical information compared to the traditionally used sample standard deviation…

We present the Shortfall Deviation Risk (SDR), a risk measure that represents the expected loss that occurs with certain probability penalized by the dispersion of results that are worse than such an expectation. SDR combines Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce, contemplating t…

The paper analyzes how SGD visits different regions of a non-convex problem's state space.

Short proof shows how ridge regression works with random data.

The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a cohe…

We provide a full characterisation of the large-maturity forward implied volatility smile in the Heston model. Although the leading decay is provided by a fairly classical large deviations behaviour, the algebraic expansion providing the higher-order terms highly depends on the parameters, and different powers of the m…

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…

We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral t…

Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.

Submodularity is studied for convex risk measures, including Expected Shortfall.

We prove that Alexandrov's conjecture relating the area and diameter of a convex surface holds for the surface of a general ellipsoid. This is a direct consequence of a more general result which estimates the deviation from the optimal conjectured bound in terms of the length of the cut locus of a point on the surface.…

We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion is given by an averaged ordinary differential equation. We then demonstrate that…

New algorithms ensure reproducibility and optimal convergence in convex optimization.

Revisits PCA with new formulations and insights.

Study short-maturity Asian option pricing in LSV models using large deviations theory.

Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to approximate the tensor rank with the $\ell_1-$norm of singular values based on its …

Optimizes riskmetrics with uncertainty, making complex problems simpler.

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly incorporates row and column features, smoothing kernels, and other sources of sid…

Develops a privacy-preserving algorithm for sparse robust regression.

Improves risk and variability measures continuity and consistency.

Adaptive exploration scheme for evaluating multiple policies with different rewards.

Unified analysis of multi-attribute graph learning with non-convex penalties.

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.

The paper addresses risk sharing and variability measures among agents with general risk preferences.

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.

We study the generalization performance of online learning algorithms trained on samples coming from a dependent source of data. We show that the generalization error of any stable online algorithm concentrates around its regret--an easily computable statistic of the online performance of the algorithm--when the underl…

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…

Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned and usually over-completed dictionary instead of a pre-defined basis. Determining …

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.

Improved Markowitz method handles uncertainty in return forecasts.

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