Unified asymptotic treatment for VaR- and expectile-based systemic risk measures.
problem Analyzing systemic risk measures under extreme system-wide disasters.
method Classified systemic risk measures into VaR- and expectile-based families, introduced new ICE and SICE measures, and provided second-order asymptotic results.
result Second-order asymptotics provide more accurate tail approximations for systemic risk measures.
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.
Study tail behavior of sum of heavy-tailed risks with copulas.
problem Analyzing the tail behavior of sums of heavy-tailed risks with dependence modeled by copulas.
method Modeling dependence with copulas and analyzing tail asymptotics of sums of heavy-tailed risks.
result Obtained asymptotic expansions for Value-at-Risk of aggregate risk.
Develops a new risk measure for Markov chains' asymptotic behavior.
problem Lack of risk measures for asymptotic regimes of Markov chains.
method Simulation-based approach using large deviations theory, density estimation, and stochastic approximation.
result Developed Asymptotic CVaR (ACVaR) for Markov chains.
Paper studies second order tail probabilities in risk models.
problem Analyzing tail probabilities in risk models with constant interest force.
method Asymptotic expansion and weighted Kesten-type inequality for second order subexponential random variables.
result Second order asymptotic formulae for continuous-time renewal risk models are derived.
Paper improves risk estimation for extreme events.
problem Estimating extreme risks accurately.
method Modified Bayes risk for expectiles, asymptotic expansions, efficient estimators.
result Asymptotic normality of estimators proved.
The paper analyzes systemic risk in an insurance model with multiple business lines and heterogeneous claims.
problem Analyzing systemic risk in a multi-dimensional insurance model with heterogeneous claims.
method A multi-dimensional Lévy process-based renewal risk model with pairwise asymptotic independence (PAI).
result Asymptotic formulas for tail probabilities and systemic risk measures are derived.
Paper examines risk measure expansions under FGM dependence, improving accuracy at extreme levels.
problem Capturing higher-order tail behavior and dependence effects in risk measures.
method Second-order asymptotic expansions using extreme value theory and regular variation theory.
result Second-order approximations reduce approximation errors, especially at extreme confidence levels.
Paper shows robust estimators converge to true risk minimizers at optimal rates.
problem Understanding asymptotic properties of robust risk minimizers.
method Investigates robust analogues of empirical risk minimization, focusing on median of means estimator.
result Robust minimizers converge to true minimizers at optimal rates and have similar asymptotic variance.
Local asymptotic minimax risk bounds in a locally asymptotically mixture of normal family of distributions have been investigated under asymmetric loss functions and the asymptotic distribution of the optimal estimator that attains the bound has been obtained.
New method improves model risk prediction using cross-audit projection.
problem Over-optimism in K-fold CV for binary classification. method Cross-audit projection (CAP) procedure combining resampling and asymptotic bias correction.
result CAP estimator achieves second-order asymptotic unbiasedness.
Paper approximates risk measures using SGD with Langevin dynamics.
problem Approximating arbitrary law invariant risk measures.
method Stochastic Gradient Langevin Dynamics (SGD-Langevin) for general risk measures.
result Non-asymptotic convergence rates of the approximation algorithm.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
The paper analyzes the risk of a least squares estimator under a spike covariance model.
problem Risk analysis of the least squares estimator under a spike covariance model.
method Assumes spike covariance matrices, studies risk as d/nightarrow∞. result Risk of the minimum norm least squares estimator vanishes compared to the null estimator.
Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g. asymptotic normality) are generally valid only for large sample-sizes, a situation rarely encountered in operational risk. In this paper, we study how…
Optimizes shortfall risk using gradient-based methods.
problem Optimizing utility-based shortfall risk measures.
method Gradient-based stochastic optimization, non-asymptotic bounds derivation.
result Non-asymptotic convergence rate for optimizing UBSR.
Optimizes diversification in catastrophe risk pooling using asymptotic analysis.
problem Maximizing diversification benefit from catastrophic events in insurance pools.
method Asymptotic analysis to solve high-dimensional optimization problem.
result Derives an asymptotically optimal pool that approximates practical optimal pool.
The paper analyzes the excess risk of PCA and provides a precise characterization.
problem Understanding the excess risk of principal component analysis (PCA).
method Established a central limit theorem for PCA error and derived the excess risk distribution.
result Obtained a non-asymptotic upper bound on the excess risk of PCA.
We consider the maximum likelihood (Viterbi) alignment of a hidden Markov model (HMM). In an HMM, the underlying Markov chain is usually hidden and the Viterbi alignment is often used as the estimate of it. This approach will be referred to as the Viterbi segmentation. The goodness of the Viterbi segmentation can be me…
Study investigates asymptotic risk of overparameterized models, including deep neural networks.
problem Understanding the risk of overparameterized models, especially deep neural networks.
method Analyzes the upper bound of an asymptotic risk of an estimator with penalization, combining Fisher information matrix properties and extended Marchenko-Pastur law.
result Generalized results valid for models without linear-in-feature constraints, indicating small asymptotic risk for specific structures like divisibility.
Derives derivatives of risk measures for various types of portfolio losses.
problem Calculating precise risk measures for portfolio losses.
method Analyzes first and second order derivatives of risk measures for both continuous and discrete portfolio loss scenarios.
result Provides asymptotic results for conditional moments of heavy-tailed portfolio losses.
Framework mitigates risk non-monotonicity in high-dimensional predictions.
problem Risk non-monotonicity in high-dimensional predictions.
method Model-agnostic framework using cross-validation and data-driven methodologies (zero- and one-step).
result Modified prediction procedures achieve monotonic asymptotic risk behavior.
In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differ…
The paper analyzes the risk of CV-tuned regularized estimators and connects it to SURE.
problem Understanding the risk of CV-tuned regularized estimators.
method Derives asymptotic risk function of CV-tuned estimators and connects it to SURE.
result The risk function provides a more detailed picture of predictive performance than uniform bounds.
The paper studies risk-based prices in financial markets under volatility uncertainty.
problem Risk-based indifference prices in financial markets under volatility uncertainty.
method Asymptotic analysis of risk-based prices in discrete-time financial markets.
result Risk-based prices form a strongly continuous convex monotone semigroup.
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.
This paper improves the Diversification Quotient (DQ) for better risk management.
problem Improving portfolio diversification measurement.
method Empirical estimation of DQ using VaR and ES, with asymptotic properties verified.
result Empirical DQ estimators are more robust and have better asymptotic properties.
Study a dual risk model with innovation delays, focusing on ruin probability and time.
problem Analyzing risk models with innovation delays affecting ruin probability and time.
method Delayed dual risk model with innovation delays, focusing on ruin probability and time.
result Closed-form formulas for ruin probability and time in some special cases.
Prove non-asymptotic bounds for minimal risk in statistical learning
problem Estimating minimal risk in statistical learning
method Using concentration inequalities
result Non-asymptotic bounds for minimal risk
The paper uses EVT to improve tail risk measures under ambiguity sets.
problem Misspecification of tail risk measures leads to inflated risk estimates.
method Applies Extreme Value Theory to derive worst-case tail risk under ambiguity sets.
result Proposes a tail-calibrated ambiguity design that preserves nominal tail asymptotic scaling.
Estimates and optimizes UBSR risk in recursive settings.
problem Estimating and optimizing UBSR risk in a recursive setting with one-at-a-time samples.
method Casts UBSR as a root finding problem, uses stochastic approximation and gradient descent.
result Derives non-asymptotic bounds on estimation and optimization errors.
Paper introduces new risk measures for Kelly criterion.
problem Aggressive Kelly criterion investment strategy.
method Unified approach to risk assessment in Kelly criterion.
result Two new measures for quantifying risk.
For a risk vector V, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…
Risk contagion concerns any entity dealing with large scale risks. Suppose (X,Y) denotes a risk vector pertaining to two components in some system. A relevant measurement of risk contagion would be to quantify the amount of influence of high values of Y on X. This can be measured in a variety of ways. In this paper, we…
In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere…
We improve prediction risk estimation for large datasets using sketching and ridge regression.
problem Estimating prediction risks for large datasets efficiently and accurately.
method Random matrix theory, generalized cross validation, sketched ridge regression ensembles, and ensemble trick.
result Consistent risk estimation and prediction intervals for large-scale datasets.
In this paper we discuss the asymptotic behaviour of random contractions X=RS, where R, with distribution function F, is a positive random variable independent of S∈(0,1). Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X…
We investigate a multi-factor extension of the asymptotic single risk factor (ASRF) model that underlies the capital charges of the "Basel II Accord". In this extended model, it is still possible to derive closed-form solutions for the risk contributions to Value-at-Risk and Expected Shortfall. As an application of the…
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
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. ERM performs well in feature learning with minimal feature maps.
problem Empirical risk minimization in feature learning with square loss.
method Asymptotic and non-asymptotic analysis of ERM performance.
result Excess risk quantiles of ERM match those of oracle procedure under certain conditions.
Paper uses stochastic algorithms to estimate systemic risk measures.
problem Estimating systemic risk measures in interconnected financial systems.
method Uses stochastic algorithms to estimate MSRM and proves consistency and asymptotic normality.
result Consistent and asymptotically normal estimators of MSRM are obtained.
The study calculates the risk of semi-supervised multitask learning on Gaussian mixtures.
problem Understanding the risk in semi-supervised multitask learning on Gaussian mixtures.
method Statistical physics methods applied to Gaussian mixture models.
result The study evaluates the performance gain of learning tasks together versus separately.
We study the asymptotic behavior of the difference ΔραX,Y:=ρα(X+Y)−ρα(X) as α→1, where ρα is a risk measure equipped with a confidence level parameter 0<α<1, and where X and Y are non-negative random variables whose tail probability functions are regularly varying. The case where …
Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.
The paper examines how heavy-tailed risks behave under Gaussian copula models.
problem Understanding tail risk probabilities with heavy-tailed marginal risks and Gaussian dependence.
method Modeling heavy-tailed risks using regular variation and analyzing tail probabilities under Gaussian copula.
result The rate of decay of tail set probabilities varies with the type of tail sets and Gaussian correlation matrix.
Paper develops Monte-Carlo estimators for CoVaR, a key risk measure.
problem Estimating CoVaR, a critical risk measure in finance.
method Developed Monte-Carlo and importance-sampling estimators for CoVaR.
result Optimal rates of convergence for both estimators: n−1/3 and n−1/2. Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.