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.
Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.
problem Understanding extreme-case risk measures under distributional ambiguity and increasing failure rate.
method Characterized extreme-case range Value-at-Risk under mean and variance constraints with increasing failure rate.
result Characterized specific characteristics of extreme-case distributions under IFR constraints.
Paper quantifies distortion risk measures' robustness to distributional uncertainty.
problem Quantifying risk measures' robustness to distributional uncertainty.
method Employing isotonic projections, the paper derives bounds on distortion risk measures' values.
result Sharp bounds on distortion risk measures' values are provided, especially for Value-at-Risk and Range-Value-at-Risk.
The paper analyzes extreme risk measures with limited distributional information.
problem Investigating risk measures under partial knowledge of distribution moments and shape.
method Employing probability inequalities and modified Schwarz inequality to derive bounds on distortion risk measures.
result Unified framework for calculating best- and worst-case scenarios of distortion risk measures.
We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The…
The paper analyzes the risk of investing in a basket of 27 cryptocurrencies using statistical distributions.
problem Risk assessment of capital allocation in a basket of cryptocurrencies.
method Used statistical tests to determine the most appropriate distribution (SDI) for modeling returns, and adapted the generalized Pareto distribution for tail risk assessment.
result Found that a combination of stable and generalized Pareto distributions provides a more accurate risk assessment for the basket of cryptocurrencies.
Sharp bounds for distortion risk metrics under uncertain distributions.
problem Modeling risk metrics under distributional uncertainty.
method Established bounds for distortion risk metrics using specific features of underlying distributions.
result Identified worst- and best-case values of distortion risk metrics.
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
The paper studies robust risk measures with linear penalties under uncertain distributions.
problem Risk measurement under distributional uncertainty.
method Robust distortion risk measures with linear penalty function under distributional constraints.
result Explicit characterization of optimal quantile distribution and value function.
The paper derives risk measures for metalog distributions.
problem Deriving risk measures for metalog distributions.
method Closed-form expressions for Conditional Value at Risk and first-order partial moments.
result First-order partial moments are convex with respect to metalog parameters.
Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In this paper we study a model where agents posses different levels of risk aversion,…
In this paper, we generalize the parametric delta-VaR method from portfolios with normally distributed risk factors to portfolios with elliptically distributed ones. We treat both the expected shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a multivariate t-distr…
Insurance benefits risk sharing for finite mean risks but not for infinite mean risks.
problem The effect of risk sharing and diversification for infinite mean risks.
method Investigation of risk sharing and diversification for infinite mean models, including stable, Pareto, and Fréchet distributions.
result Risk sharing can have a negative effect for infinite mean models, a phenomenon known as the nondiversification trap.
A new framework tightens risk measure confidence bounds.
problem Improving confidence bounds for various risk measures.
method Distribution optimization framework with two estimation schemes based on concentration bounds.
result Consistently tighter confidence bounds compared to previous methods.
Paper proposes robust risk measures for non-negative risks with partial information.
problem Tackles robustness of distortion risk measures under distributional uncertainty.
method Introduces new uncertainty sets and derives closed-form expressions for risk maximization.
result Derives closed-form expressions for risk maximization over uncertainty sets.
Risk measures applied to dynamic Markov processes with varying risk aversion.
problem Investigating dynamic risk measures in Markov decision processes with varying risk aversion.
method Distributional viewpoint on law-invariant convex risk measures, applied to Markov decision processes with latent costs and random actions.
result Existence of optimal policies in finite and infinite time horizons under mild assumptions.
EX-DRL improves extreme quantile prediction for financial risk management.
problem Inaccurate estimation of extreme quantiles in loss distributions.
method EX-DRL uses Generalized Pareto Distribution (GPD) to model the tail of the loss distribution and Quantile Regression (QR) to improve extreme quantile prediction.
result EX-DRL provides more precise estimates of extreme quantiles, improving risk metrics reliability.
Study optimal portfolio selection with Recovery Average Value at Risk, showing better control over liabilities.
problem Optimizing portfolios with a new risk measure under known or uncertain distributions.
method Existence results for mean-risk optimal portfolios under different distributional assumptions.
result Portfolio selection under Recovery Average Value at Risk provides better control over liabilities.
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.
Researchers calculated EVaR for various distributions using Lambert function.
problem Difficulty in finding analytical representation of EVaR measure.
method Used Lambert function to calculate EVaR for multiple distributions.
result Successfully calculated EVaR for 7 specific distributions.
The paper introduces MRVaR and MRCov for elliptical and log-elliptical distributions.
problem Risk management of regulation and investment purposes.
method Proposes MRVaR and MRCov as risk measures for elliptical and log-elliptical distributions.
result Explicit expressions of MRVaR and MRCov derived for multivariate (log-)elliptical distributions.
Paper analyzes cyber risk classifications for forecasting performance.
problem Lack of effective out-of-sample forecasting performance in current cyber risk classifications.
method Rolling window analysis using threshold weighted scoring functions.
result Dynamic and impact-based cyber risk classifiers outperform others in forecasting future cyber risk losses.
This paper uses multivariate probability models to assess financial system risks.
problem Assessing systemic risk in financial systems.
method Computes multivariate conditional probability distributions for elliptical distributions, focusing on Student-t and Normal models.
result Proposes measures of stress impact and systemic risk.
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.
New method for risk allocation under multimodality of loss distribution.
problem Risk assessment under multimodal conditional loss distribution.
method Maximum Likelihood Allocation (MLA) and multimodality adjustment.
result Multimodality adjustment improves soundness of risk allocations.
Optimizes forecast distributions for financial risk management.
problem Improving risk management through better forecast distributions.
method Optimizes forecast distributions using scoring rules relevant to financial risk management.
result Tail-focused predictive distributions yield better outcomes in hedging strategies involving VIX futures.
In this paper, we generalize the parametric Delta-VaR methods from portfolios with elliptic distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of the mixtur…
New method uses asymmetric Tsallis relative entropy for better risk assessment in financial portfolios.
problem Improving risk assessment for financial portfolios using asymmetric data.
method Generalized Tsallis relative entropy (ATRE) for asymmetric distributions of returns.
result ATRE shows better risk-return profiles, especially during market crashes.
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.
MaxRM uses random forests to minimize maximum risk across different environments.
problem Designing methods that generalize better to test environments with different distributions.
method Introducing variants of random forests based on the principle of MaxRM (Maximum Risk Minimization).
result Proved statistical consistency for the proposed method and provided an out-of-sample guarantee for MaxRM with regret.
We introduce a class of dependence structures, that we call the Multiple Risk Factor (MRF) dependence structures. On the one hand, the new constructions extend the popular CreditRisk+ approach, and as such they formally describe default risk portfolios exposed to an arbitrary number of fatal risk factors with condition…
Paper proposes a new DRL algorithm optimizing Spectral Risk Measures for better risk management.
problem Inconsistencies and conservatism in existing risk measures in DRL.
method Optimizes a broader class of static Spectral Risk Measures (SRM) in DRL.
result Demonstrates improved performance over existing risk-neutral and risk-sensitive DRL models.
Improves reinforcement learning policies for robustness.
problem Lack of robustness in reinforcement learning policies.
method Risk-aware Distributional Reinforcement Learning (SDPG) with CVaR.
result Risk-averse policies achieve robustness against disturbances.
This paper unifies risk-averse Thompson sampling for continuous risk functionals.
problem Designing and analyzing risk-averse Thompson sampling algorithms for continuous risk functionals.
method Developed analytical toolkits to prove asymptotically optimal regret bounds for various risk measures.
result Proved asymptotic optimality of ρ-MTS for Bernoulli distributions and a class of risk measures. We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined via application of several statistical tests and risk measures. The results indi…
New risk class defined based on loss location and deviation.
problem Risk assessment in loss distributions.
method Wrapper around smooth loss functions, M-estimators, stochastic gradient methods.
result Finite-sample stationarity guarantees for stochastic gradient methods.
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.
This paper proves IRM minimizes o.o.d. risk under certain conditions.
problem Deep networks can fail to generalize to new domains with different distributions.
method Proves IRM minimizes o.o.d. risk through a bi-level optimization problem.
result IRM minimizes o.o.d. risk under specific conditions.
Regulation and risk management in banks depend on underlying risk measures. In general this is the only purpose that is seen for risk measures. In this paper we suggest that the reporting of risk measures can be used to determine the loss distribution function for a financial entity. We demonstrate that a lack of suffi…
REx tackles distributional shift by reducing risk differences across domains.
problem Tackling distributional shift when transferring machine learning systems to real-world applications.
method Risk Extrapolation (REx) assumes training domains represent test-time variations and uses extrapolated domains to minimize risk variance.
result REx reduces sensitivity to extreme distributional shifts, including causal and anti-causal inputs.
The paper extends risk measures to two-step approximations and studies log-concave distributions.
problem Extending classical risk measures to two-step approximations.
method Optimization problem for determining optimal regime thresholds and values for log-concave distributions.
result Conditions for the uniqueness of regime changing in log-concave distributions.
This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …
New method uses DistRL to estimate entire payoff distribution for financial derivatives.
problem Traditional methods focus on expected option value; this tackles risk-aware pricing.
method Reinterprets and proposes a framework using Distributional Reinforcement Learning (DistRL).
result Demonstrates enhanced risk-aware pricing and uncertainty quantification on Asian options.
Paper proposes MMW distribution for better financial risk modeling.
problem Modeling non-normal stock returns for risk estimation.
method Mixture of mirrored Weibull (MMW) distribution for flexible risk modeling.
result MMW model outperforms Gaussian and t-mixture models in VaR estimation.
To quantify an operational risk capital charge under Basel II, many banks adopt a Loss Distribution Approach. Under this approach, quantification of the frequency and severity distributions of operational risk involves the bank's internal data, expert opinions and relevant external data. In this paper we suggest a new …
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation ineq…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a random variable with an elliptical distribution and the notion of portfolio risk is d…
Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern comput…