Study asymptotic properties of generalized shortfall risk measures for heavy-tailed risks.
problem Understanding risk measures for heavy-tailed risks.
method Derive asymptotic expansions for generalized shortfall risk measures.
result Unified theory for risk measures including distortion and utility-based measures.
Generative Adversarial Regression (GAR) learns risk scenarios robustly across policies.
problem Learning risk scenarios for conditional risk objectives.
method Generative adversarial framework for risk matching.
result GAR produces more stable and risk-preserving scenarios than baselines.
New risk measure considers horizon risk and interest rate uncertainty.
problem Dynamic risk evaluation considering horizon risk and interest rate uncertainty.
method Introduced a risk measure based on generalized Tsallis entropy.
result New q-entropic risk measure quantifies capital requirement.
The paper establishes a connection between different risk measures and their risk contributions.
problem Understanding the relationship between conditional coherent and deviation risk measures.
method Axiomatic framework and continuous-time risk contribution analysis.
result Risk contributions of time-consistent risk measures are also time-consistent.
Develops uniform convergence guarantees for a broad class of risk functionals in supervised learning.
problem Bounding generalization gaps for various risk functionals beyond the expectation.
method Establishes uniform convergence for Hölder risk functionals, providing guarantees for empirical risk minimization.
result First uniform convergence results for estimating the CDF of loss distributions, applicable to various risk functionals.
Generalizes risk sharing models to a continuum of agents.
problem Risk sharing among a large number of heterogeneous agents.
method Modeling agents as points in a measure space, using risk measures on a probability space, and deriving dual representations.
result Explicit formulas for specific risk measures (entropic and expected shortfall) and applications to Pareto efficiency.
Extends inf-convolution to countable risk measures for risk sharing.
problem Limited inf-convolution theory to finite sets of risk measures.
method Extends inf-convolution to countable sets, investigates properties and results.
result Generalizes known properties and results to countable case.
This paper introduces new risk measures for evaluating losses with varying time horizons.
problem Capturing horizon risk and cash non-additivity in risk evaluation.
method Uses BSDEs and shortfall approaches to develop h-generalized shortfall risk measures.
result Introduces hq-entropic risk measures as a new family of fully-dynamic risk measures.
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and behavioral economics. Within the framework, applying weighted norm spaces to incorporate …
We give a complete algorithm and source code for constructing general multifactor risk models (for equities) via any combination of style factors, principal components (betas) and/or industry factors. For short horizons we employ the Russian-doll risk model construction to obtain a nonsingular factor covariance matrix.…
Sharp bounds found for various risk measures using generalized FGM copulas.
problem Finding sharp bounds for risk measures in high dimensions.
method Proved that generalized FGM copulas form a convex polytope, used this structure to find bounds for risk measures.
result Sharp analytical bounds for convex risk measures in the class of generalized FGM copulas.
Paper introduces quasi-logconvex risk measures and their properties.
problem Characterizing and understanding new risk measures.
method Characterization through dual representation and properties of acceptance sets.
result Established dual representation and taxonomy of quasi-logconvex risk measures.
Paper uses a new copula to model risk aggregation and capital allocation.
problem Modeling dependence between risks for risk aggregation and capital allocation.
method Uses a generalized Archimedean copula (mixed Bernstein copula) to define dependence structure and derives closed-form risk measures.
result Closed-form expressions for tail value-at-risk and allocations are derived.
New risk measures control subgroup imbalances, improving PAC-Bayesian bounds.
problem Insufficient risk bounds for subgroup imbalances in data.
method Introduce constrained f-entropic risk measures and derive PAC-Bayesian bounds.
result First disintegrated PAC-Bayesian guarantees beyond standard risks.
New risk measure and quadrangle improve financial decision-making.
problem Heterogeneous risk assessments among analysts.
method Established analytical characterizations of WGRM and incorporated FRQ into WRQ.
result WGRM and WRQ framework improves risk-adjusted performance and downside resilience.
Study risk-sensitive reinforcement learning with entropic risk measures and generative models.
problem Risk-sensitive reinforcement learning in discounted MDPs with recursive entropic risk measures.
method Introduced Model-Based ERM Q-Value Iteration (MB-RS-QVI) and derived PAC bounds on sample complexity for value and policy learning. result PAC bounds show exponential dependence on ∣β∣/(1−γ), with tight bounds in S and A. New conditional risk measures called conditional generalized quantiles defined and characterized.
problem Developing new risk measures for dynamic risk assessment.
method Propose and characterize conditional generalized quantiles using expected utility model and equivalent conditions.
result Characterized conditional generalized quantiles as well-defined and equivalent to a conditional first order condition.
GAICF proposes a framework for managing generative AI risks in banking.
problem Generative AI's impact on financial decision-making and governance.
method SR 26-2-compatible governance framework for generative AI.
result GAICF aligns generative AI practices with SR 26-2 supervisory expectations.
Unified framework for risk evaluation under uncertainty.
problem Risk assessment under multiple economic scenarios.
method Axiomatic framework for generalized risk measures.
result Characterization of worst-case, coherent, and robust risk measures.
Practical application of Reinforcement Learning (RL) often involves risk considerations. We study a generalized approximation scheme for risk measures, based on Monte-Carlo simulations, where the risk measures need not necessarily be \emph{coherent}. We demonstrate that, even in simple problems, measures such as the va…
New star-shaped acceptability indexes generalize existing methods.
problem Generalizing existing acceptability measures.
method Characterizing acceptability indexes through star-shaped risk measures and sets.
result Introducing concrete examples linked to various financial measures.
Paper establishes identifiability and elicitability of tail risk measures.
problem Identifying and measuring tail risk measures accurately.
method Establishes identifiability and elicitability of tail risk measures using generators and quantiles.
result Joint identifiability and elicitability of tail risk measures and quantiles.
Generative neural networks improve insurance market risk modeling.
problem Creating realistic market risk scenarios for insurance companies.
method Using generative adversarial networks (GANs) to generate economic scenarios.
result GAN-based models produce similar results to traditional regulatory models.
Study examines risk premium convergence rates in risk sharing contracts.
problem Analyzing risk premium convergence rates in risk sharing contracts.
method Examines the limiting behavior of risk premium associated with Pareto optimal risk sharing contracts under general law-invariant risk measures.
result Risk premium convergence rate is typically n1/2, not n. Optimizes asset allocation for risk measures in a Lévy market.
problem Maximizing time-consistent mean-risk reward with general risk measures.
method Uses a generalized Lévy market model and Hamilton-Jacobi-Bellman equation.
result Deterministic optimal solution under certain conditions.
The paper examines the tilted empirical risk's generalization and robustness under negative tilt.
problem The generalization error of machine learning algorithms under negative tilt.
method Uniform and information-theoretic bounds on the tilted generalization error under negative tilt.
result The tilted empirical risk's generalization error has a convergence rate of \(O(n^{-ε/(1+ε)})\).
We generalize Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Tail Value at Risk and the Entropic Risk Measure in a unified way. We then investigate the fundamental propert…
Financial institutions face new model risks with AI, requiring enhanced model risk management.
problem New model risks from Generative AI applications in financial institutions.
method Enhanced model risk framework with additional testing and controls.
result Financial institutions need to enhance their model risk management for Generative AI applications.
Study finds high cyber risk stocks generate significant excess returns.
problem Understanding and quantifying cyber risk's impact on stock returns.
method Machine learning algorithm measuring cyber risk proximity to a corpus.
result High cyber risk stocks generate an excess return of 18.72% p.a.
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
Study improves summarization reliability in risky scenarios.
problem Reliability of automatic summarization in high-risk contexts.
method Conditional generation with Bayesian inference and entropy regularization.
result Significant improvement in robustness and reliability of summarization.
New method tests risk measures for various distortions.
problem Testing risk measures for different distortions.
method Stratification and randomization of risk levels.
result Method performs well in numerical case studies.
Financial institutions have to allocate so-called "economic capital" in order to guarantee solvency to their clients and counter parties. Mathematically speaking, any methodology of allocating capital is a "risk measure", i.e. a function mapping random variables to the real numbers. Nowadays "value-at-risk", which is d…
Study uses generative models to assess credit risk and determine loan sizes in e-commerce supply chain finance.
problem Credit risk assessment and loan size determination for small- and medium-sized sellers in e-commerce supply chain finance.
method Proposes a unified framework using Quantile-Regression-based Generative Metamodeling (QRGMM) integrated with Deep Factorization Machines (DeepFM) to capture complex covariate interactions in e-commerce sales data.
result Validates the model's efficacy for credit risk assessment and loan size determination on synthetic and real-world data.
The paper studies risk-sensitive learning schemes and provides learning bounds for empirical OCE minimizers.
problem Risk-sensitive learning aims to minimize risk-averse measures of loss.
method Proposes learning bounds for empirical OCE minimizers based on Rademacher average and variance.
result Provides two learning bounds on the performance of empirical OCE minimizers.
We study risk-sensitive imitation learning where the agent's goal is to perform at least as well as the expert in terms of a risk profile. We first formulate our risk-sensitive imitation learning setting. We consider the generative adversarial approach to imitation learning (GAIL) and derive an optimization problem for…
The paper examines the feasibility of managing aggregate cyber-risk in IoT environments.
problem Determining sustainable conditions for providing aggregate cyber-risk coverage.
method Developed a rigorous general theory and validated it with real data.
result Conditions for sustainable aggregate cyber-risk management under heavy-tailed distributions.
Study risk sharing among agents with varying risk preferences.
problem Risk sharing among agents with heterogeneous risk measures.
method Derive explicit solutions for inf-convolution and counter-monotonic inf-convolution under varying risk seeking.
result Explicit solutions for inf-convolution and counter-monotonic inf-convolution can be represented by a generalization of distortion risk measures.
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
Study non-asymptotic bounds for robust estimators under misspecified models.
problem Evaluate performance of robust estimators under adversarial conditions.
method Propose a general approach to adversarial risk analysis, including investigations on generalization and approximation errors.
result Establish non-asymptotic upper bounds for adversarial excess risk under Lipschitz loss functions.
Paper tackles heavy-tailed data without finite variance, proposing robust risk minimization.
problem Empirical risk minimization under heavy-tailed data with finite p-th moment. method Minimizes risk values robustly estimated via Catoni's method, using generalized generic chaining.
result Shows better performance of optimizer based on empirical risks via Catoni-style estimation.
Proposes a new framework for environmental CVA with robust wrong-way risk.
problem Limited operational implementations of translating environmental scenarios into CVA.
method Three components: hazard rate mapping, tail generators, and KL divergence-based wrong-way risk bound.
result Nature CVAs can vary significantly across different ecosystem generators.
Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.
problem Limited theoretical analysis for distributed ERM with general loss functions and hypothesis spaces.
method Derive tight risk bounds under assumptions on hypothesis space and loss function.
result Developed more general risk bound for distributed ERM without strong convexity restriction.
Modern society heavily relies on strongly connected, socio-technical systems. As a result, distinct risks threatening the operation of individual systems can no longer be treated in isolation. Consequently, risk experts are actively seeking for ways to relax the risk independence assumption that undermines typical risk…
The risk premium of a policy is the sum of the pure premium and the risk loading. In the classification ratemaking process, generalized linear models are usually used to calculate pure premiums, and various premium principles are applied to derive the risk loadings. No matter which premium principle is used, some risk …
The paper addresses risk sharing and variability measures among agents with general risk preferences.
problem Risk sharing and variability measures among agents with general risk preferences.
method Characterizes Pareto-optimal allocations using Gini deviation, mean-median deviation, and inter-quantile difference as variability measures.
result Optimal allocations are not comonotonic and feature a mixture of pairwise counter-monotonic structures.
Simple conditions for comonotonic additive risk measures from acceptance sets.
problem Conditions for comonotonic additive risk measures from acceptance sets.
method Conditions on acceptance sets for induced comonotonic additive risk measures.
result Acceptance sets induce comonotonic additive risk measures if and only if the acceptance sets and their complements are stable under convex combinations of comonotonic random variables.
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional aggregation and a univariate conditional risk measure. Our studies extend known results f…