We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
Trend · papers per month
48 results for “expected distortion”
ReLU networks don't exponentially distort curve lengths as previously thought.
problem Understanding how neural networks distort curve lengths with depth.
method Analyzing expected length distortion of ReLU networks with random initialization.
result Expected length distortion does not grow with depth, and shrinks slightly.
On evaluation of joint risk for non-negative multivariate risks under dependence uncertaintyq-fin.RM
Paper proposes a new method to evaluate joint risk under uncertainty.
problem Evaluating joint risk of multiple insurance risks under dependence uncertainty.
method Axiomatic approach to scalar and vector-valued distortion joint risk measures.
result Established a new scalar distortion joint risk measure with positive homogeneity.
Paper introduces new risk norms based on ES with flexible distortion functions.
problem Risk quantification and anomaly detection in financial data.
method Developed generalized Expected-Shortfall (ES) norms using distortion risk measures and duality theory.
result Unified analytical framework for risk quantification and practical applications.
Optimal insurance strategy for maximizing RDEU under various premium principles.
problem Maximizing a risk-averse individual's RDEU with insurance priced by a distortion-deviation principle.
method Proved necessary and sufficient conditions for the optimal solution, considered ambiguity orders, and analyzed specific examples.
result Conditions for no insurance or deductible insurance to be optimal.
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…
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 paper analyzes risk measures and optimal reserve allocation strategies.
problem Risk measures and optimal reserve allocation across multiple lines of business.
method Formalizes expected maximum deficit, introduces implicitly bounded risk measures, and proposes capital allocation approaches.
result Theoretical results on static and dynamic coherence, convexity, and exact optimizations of aggregate minimum reserves.
New bounds for optimal transport using Gaussian processes and rate-distortion functions.
problem Finding bounds for entropic optimal transport with mutual information constraints.
method Lifting technique to construct a Gaussian process and applying the majorizing measure theorem.
result Maximum expected inner product is equivalent to a truncated integral involving the rate-distortion function.
New concept of partial comonotonicity connects riskmetrics and dependence.
problem Understanding and quantifying risk metrics under partial comonotonicity.
method Developed a new notion of partial comonotonicity and established its connection to distortion riskmetrics.
result Partial comonotonicity uniquely characterizes a class of distortion riskmetrics through additivity.
Optimizes riskmetrics with uncertainty, making complex problems simpler.
problem Optimizing riskmetrics with distributional uncertainty.
method Unifying result converting non-convex optimization to convex, using closedness under concentration.
result Great tractability achieved through unifying equivalence result.
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward distributions: the classic -armed bandit and the linearly parameterized bandit…
Stochastic measure distortions induced by quantile processes for risk quantification and valuationq-fin.RM
New method for risk quantification using quantile processes and measure distortions.
problem Risk quantification and valuation in financial markets.
method Develops a novel stochastic valuation principle based on probability measure distortions induced by quantile processes.
result Introduces a system of subjective probability measures that indexes a stochastic valuation principle susceptible to probability measure distortions.
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and r…
Extends likelihood ratio exponential families to analyze various optimization methods.
problem Analyzing optimization methods like rate-distortion and information bottleneck.
method Linking geometric mixture paths to exponential families and using hypothesis testing.
result Provides a common mathematical framework for understanding these methods.
Proposes ITISC for clustering with minimized worst-case expected distortions.
problem Real-world clustering data distribution mismatch.
method Information theoretical importance sampling, constrained minimax optimization, Lagrange method.
result Validation of ITISC on synthetic and real-world datasets.
New framework uses cohomology to analyze probabilistic distortions and arbitrage.
problem Analyzing probabilistic distortions and arbitrage in categorical filtrations.
method Transport cohomological framework, simplicial structure, loop effects, holonomy.
result Nontrivial probabilistic distortions and obstructions generated by loops.
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…
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Study models weather index insurance pricing by insurers and farmers, finding flexible pricing kernels boost profits.
problem Monopoly pricing of weather index insurance with risk and flexibility considerations.
method Bowley-type sequential game with insurer and farmer, using neural networks for farmer's payoff.
result Flexible pricing kernels increase insurer profits closer to indemnity insurance levels.
Method determines asset prices in incomplete markets to optimize portfolios.
problem Optimizing portfolios in incomplete markets with price constraints.
method Maximum entropy in the mean to adjust distortion function from bid-ask data.
result Prices of assets comply with portfolio optimization constraints.
Aggregation distorts causal discovery results but recovery is possible with partial linearity or prior.
problem Understanding how temporal aggregation affects causal discovery in aggregated data.
method Functional consistency and conditional independence consistency methods.
result Causal discovery results may be distorted by aggregation, but recovery is possible with certain conditions.
Submodular risk measuresq-fin.RM
Submodularity is studied for convex risk measures, including Expected Shortfall.
problem Characterizing submodularity in convex risk measures.
method Analyzing submodularity properties of law-invariant coherent risk measures, including Expected Shortfall and Value-at-Risk.
result AES is submodular only when it reduces to ES, and empirical analysis shows AES violations are less frequent than VaR and ES violations.
New framework uses simplicial and categorical methods to detect market inconsistencies.
problem Detecting inconsistencies in financial markets using non-measure-preserving transitions.
method Simplicial and categorical formulation of AB type arbitrage in filtered market systems.
result Holonomy along loops reveals global inconsistencies invisible at local levels.
Unified bounds linking compressibility, fractal dimensions, and mutual information.
problem Understanding generalization in stochastic learning algorithms.
method Rate-distortion theory applied to machine learning generalization.
result Unified bounds linking compressibility, fractal dimensions, and mutual information.
Vertex distortion detects if a knot is unknot.
problem Determining if a knot is the unknot.
method Using Denne-Sullivan's bound on Gromov distortion, the vertex distortion of nontrivial lattice knots is bounded. Then, it is shown that trivial vertex distortion implies the unknot.
result The conjecture that trivial vertex distortion implies the unknot is proven.
We characterize when a convex risk measure associated to a law-invariant acceptance set in can be extended to , , preserving finiteness and continuity. This problem is strongly connected to the statistical robustness of the corresponding risk measures. Special attention is paid to concre…
Efficiently simulates risk budgeting portfolios using novel algorithms.
problem Estimating risk contributions in portfolios efficiently.
method Cutting planes algorithm, specialised SGD for Expected Shortfall, numerical simulations.
result Outperforms standard convex optimisation solvers in estimating risk budgeting portfolios.
Algorithm finds optimal affine transformation to minimize overall distortion.
problem Minimizing distortion in affine transformations.
method Riemannian geometry approach to define and minimize distortion.
result Mean distorting transformation found for minimizing overall distortion.
Optimizes portfolio growth rate for a behavioral investor considering terminal relative growth rate.
problem Optimizing a behavioral investor's portfolio growth rate under relative growth criterion.
method Martingale method, concavification, and quantile optimization techniques.
result Derives closed-form optimal growth rate and finds significant impact of benchmark growth rate.
Maxout networks study gradients and propose initialization strategies.
problem Complexity in input-output Jacobian distribution complicates stable parameter initialization.
method Obtained bounds on moments of gradients and formulated initialization strategies.
result Parameter initialization strategies improve training of deep maxout networks.
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected classifier score remains nearly constant when randomising the remaining features. We disc…
New method optimizes risk estimation for financial losses.
problem Estimating expected shortfall risk for heavy-tailed distributions.
method Proposes a novel estimator for expected shortfall robust to data corruption.
result Demonstrates superior performance and robustness compared to classical methods.
Vertex distortion measures how far lattice knots deviate from straight lines.
problem Measuring how much lattice knots deviate from straight paths.
method Analogous to smooth knots, study vertex distortion in lattice knots.
result Vertex distortion is 1 only for the unknot and can be arbitrarily high.
We consider the problem of distortion minimal morphing of -dimensional compact connected oriented smooth manifolds without boundary embedded in . Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
problem Calculating risk measures for sums of two counter-monotonic risks.
method Using a fixed distortion function and expressing the risk measure of a sum as the sum of two related measures of the marginals.
result The risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals.
Most distortion correction methods focus on simple forms of distortion, such as radial or linear distortions. These works undistort images either based on measurements in the presence of a calibration grid, or use multiple views to find point correspondences and predict distortion parameters. When possible distortions …
Study distortion risk measures for step-weighted distributions.
problem Analyzing risk measures for specific distribution types.
method Investigate distortion risk measures of step-weighted distributions.
result Developed methods for calculating risk measures.
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil kno…
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
CDP reduces point cloud dimensions by preserving detour-induced local non-convexity.
problem Preserving local non-convexity in point cloud dimensionality reduction.
method CDP builds a k-NN graph, identifies admissible pairs, aggregates normalized directions, and uses top-k eigenvectors for projection.
result CDP provides verifiable guarantees on post-projection distortion and direction energy.
Study optimal reinsurance pricing under model uncertainty for multiple insurers.
problem Optimal reinsurance pricing in the presence of multiple sources of model uncertainty.
method Solves a continuous-time Stackelberg game for general reinsurance contracts, considering entropy penalties and ambiguity in insurers' models.
result Reinsurer prices under a distortion of the barycentre of insurers' models, maximizing expected wealth with an entropy penalty.
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, ha…
The paper analyzes insurance pricing and capital allocation in imperfect markets.
problem Analyzing insurance pricing and capital allocation in imperfect markets.
method Non-additive distortion pricing functional and principle of equal priority of payments in default.
result Derives the natural allocation of premium and margin with properties that merit the name.
The distortion of a curve is the supremum, taken over distinct pairs of points of the curve, of the ratio of arclength to spatial distance between the points. Gromov asked in 1981 whether a curve in every knot type can be constructed with distortion less than a universal constant C. Answering Gromov's question seems to…
The study shows exponential distortion in virtually special groups containing free subgroups.
problem Understanding distortion in virtually special groups containing free subgroups.
method Constructing examples of virtually special groups with finite rank free subgroups.
result Distortion functions grow like exp^k(x^m) and can be superexponential.
Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Codingcs.IT
Estimates rate-distortion function for large datasets using neural networks.
problem Designing lossy data compression schemes and comparing them with theoretical limits.
method Re-formulate rate-distortion objective and solve using neural networks.
result NERD accurately estimates the rate-distortion function for real-world datasets.