arXiv research

This paper shows how to calculate risk measures for sums of two counter-monotonic risks.

New insights into risk aversion for complex decision models.

The paper optimizes watermarking of LLMs, improving detection ability.

We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under certain conditions on the parameters of these power functions. In the present paper w…

Optimizes riskmetrics with uncertainty, making complex problems simpler.

Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of points. We formulate the problem as a non convex constrained optimization problem. …

The expectile can be considered as a generalization of quantile. While expected shortfall is a quantile based risk measure, we study its counterpart -- the expectile based expected shortfall -- where expectile takes the place of quantile. We provide its dual representation in terms of Bochner integral. Among other prop…

Study dynamic risk measures and performance indices using distortion functions.

Estimates rate-distortion function for large datasets using neural networks.

Computed distortion coefficients for the α-Grushin plane.

New coding theorem shows achievable rate matches theoretical limit.

The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.

We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …

The study shows exponential distortion in virtually special groups containing free subgroups.

The paper calculates bounds for risk metrics and entropies under partial information constraints.

Quantized Stochastic Primal-Dual Methods for Distributed Optimization

Study on risk measures using distorted Choquet integrals with random distortions.

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…

Modified BA algorithm computes RD and DR functions efficiently.

We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The proposed encoding algorithm sequentially chooses columns of the design matrix to suc…

Sharp bounds for distortion risk metrics under uncertain distributions.

Paper proposes robust risk measures for non-negative risks with partial information.

The study finds minimal distortion embeddings of surfaces into small domains.

Let $M$ and $N$ be compact smooth oriented Riemannian $n$-manifolds without boundary embedded in $\mathbb{R}^{n+1}$. Several problems about minimal distortion bending and morphing of $M$ to $N$ are posed. Cost functionals that measure distortion due to stretching or bending produced by a diffeomorphism $h:M \to N$ are …

Paper introduces new risk norms based on ES with flexible distortion functions.

New method for risk quantification using quantile processes and measure distortions.

DP-means clustering was obtained as an extension of $K$-means clustering. While it is implemented with a simple and efficient algorithm, it can estimate the number of clusters simultaneously. However, DP-means is specifically designed for the average distortion measure. Therefore, it is vulnerable to outliers in data, …

The paper studies robust risk measures with linear penalties under uncertain distributions.

We analyze the obstruction to metrics of positive scalar curvature within a given bounded distortion class of metrics. This obstruction lives in a non-Hausdorff cohomology group Poincare dual to the uniformly finite homology studied by Block and Weinberger. One of the applications is a converse to their theorem on infi…

The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…

We solve the vector embedding problem by minimizing total distortion under constraints.

Paper studies fundamental limits of communication in distributed learning.

New bounds for optimal transport using Gaussian processes and rate-distortion functions.

Paper derives best- and worst-case GlueVaR measures with incomplete data.

Given a space $Y$ in $X$, a cycle in $Y$ may be filled with a chain in two ways: either by restricting the chain to $Y$ or by allowing it to be anywhere in $X$. When the pair $(G,H)$ acts on $(X, Y)$, we define the $k$-volume distortion function of $H$ in $G$ to measure the large-scale difference between the volumes of…

Study allocates resources to strategic agents while balancing cost and incentives.

Study the tradeoff between signal distortion and human perception over finite channels.

Paper proposes a new black-box attack approach to minimize visual distortion.

The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even if the company covers its entire costs by collecting the respective fees from i…

The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman…

We produce examples of codimension one foliations of the Euclidean and hyperbolic planes with bounded geometry which are topologically products, but for which leaves are non-recursively distorted. That is, the function which compares intrinsic distances in leaves with extrinsic distances in the ambient space grows fast…

Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…

Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.

Framework uses IRL and RL to elicit and optimize risk preferences robustly to noise.

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein d…

Given a finite metric CW complex $X$ and an element $α\in π_n(X)$, what are the properties of a geometrically optimal representative of $α$? We study the optimal volume of $kα$ as a function of $k$. Asymptotically, this function, whose inverse, for reasons of tradition, we call the volume distortion, turns out to be an…

Researchers prove inner product recovery is impossible in latent space models.