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.
The paper analyzes the performance of empirical risk minimization for p-norm linear regression.
problem Empirical risk minimization on p-norm linear regression. method Analyzes performance under various conditions and moment assumptions.
result High probability excess risk bounds for empirical risk minimizer, matching asymptotic rates.
We study the pricing and hedging of derivatives in incomplete financial markets by considering the local risk-minimization method in the context of the benchmark approach, which will be called benchmarked local risk-minimization. We show that the proposed benchmarked local risk-minimization allows to handle under extre…
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
Study risk-minimizing insurance investments with taxes and expenses.
problem Determining optimal insurance investments in the presence of taxes and expenses.
method Introduced tax- and expense-modified risk-minimization, derived strategies, linked to decompositions, and established equivalence to artificial market approach.
result Equivalence to artificial market approach and consistency with classic risk-minimization.
Paper studies convergence rates from surrogate risk minimizers to Bayes optimal classifier.
problem Analyzing the convergence rates of surrogate risk minimizers to the Bayes optimal classifier.
method Introducing consistency intensity to characterize surrogate loss functions and using it to derive convergence rates.
result Empirical surrogate risk minimizers converge faster to the Bayes optimal classifier under certain conditions.
Proposes a robust risk measure to minimize capital errors.
problem Minimizing capital determination errors due to risk overestimation and underestimation.
method Uses supremum over probability measures to minimize overestimation and underestimation costs.
result Guarantees the existence of a solution and explores properties of minimizer and minimum as risk and deviation measures.
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.
We study Spectral Measures of Risk from the perspective of portfolio optimization. We derive exact results which extend to general Spectral Measures M_phi the Pflug--Rockafellar--Uryasev methodology for the minimization of alpha--Expected Shortfall. The minimization problem of a spectral measure is shown to be equivale…
This paper explores portfolio management strategies to maximize alpha and minimize beta.
problem Maximizing returns while minimizing risk in investment portfolios.
method Examines asset allocation, diversification, active management, and risk management strategies.
result Combining these strategies optimizes portfolio performance.
This paper begins with a study on the dual representations of risk and regret measures and their impact on modeling multistage decision making under uncertainty. A relationship between risk envelopes and regret envelopes is established by using the Lagrangian duality theory. Such a relationship opens a door to a decomp…
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
This paper analyzes privacy-preserving methods for sparse model optimization.
problem Privacy-preserving sparse model optimization with non-differentiable norms.
method Differential privacy techniques applied to Frank-Wolfe and objective perturbation algorithms.
result Excess risk bounds for Frank-Wolfe and objective perturbation algorithms are derived.
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.
In portfolio optimization problems, the minimum expected investment risk is not always smaller than the expected minimal investment risk. That is, using a well-known approach from operations research, it is possible to derive a strategy that minimizes the expected investment risk, but this strategy does not always resu…
CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.
problem Traditional risk assessment methods underperform in stock market analysis.
method Derived new CV equation and used it to analyze stock performance.
result Stocks with low but positive CV grow exponentially, outperforming high-risk stocks.
Paper bounds convergence rate of adversarial surrogate risk.
problem Vulnerability of binary classification models to adversarial attacks.
method Characterizes conditions for adversarial consistency and provides surrogate risk bounds.
result Surrogate risk bounds quantify the rate of convergence of adversarial classification risk.
Paper bounds excess risk in robust empirical risk minimization for heavy-tailed distributions.
problem Risk bounds for robust empirical risk minimization in heavy-tailed distributions.
method Proposes robust proxies for expectation to bound excess risk.
result Excess risk of robust estimators can converge to 0 at fast rates.
Unified framework for shrinkage, thresholding, and regularization in normal mean estimation and linear regression.
problem Estimation of normal mean in multivariate settings with correlated observations.
method Approximate risk minimization over a functional class of shrinkage-thresholding rules.
result Unified estimator NOMAD for shrinkage, thresholding, and regularization.
Robust learning method minimizes risk with corrupted data.
problem Statistical learning with unknown corrupted data fraction.
method Develops a robust learning method with specified corrupted data fraction upper bound.
result Optimal weights provide robustness against corrupted data.
New method diversifies risk using complex numbers.
problem Minimizing portfolio risk under constraints.
method Complex valued principal component analysis in risk diversification.
result Outperforms conventional risk parity and diversification methods.
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimiz…
In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is i…
Study minimizes risk in MDPs with spectral measures.
problem Minimizing risk in MDPs with spectral measures.
method Splitting into inner and outer minimization problems; solving inner as MDP; proving existence for outer.
result Existence and solution methods for the outer minimization problem.
The paper explores risk-minimization for exponential additive models, providing mathematical expressions and numerical examples.
problem Risk-minimization in incomplete markets for exponential additive models.
method Derive explicit mathematical expressions for local risk-minimization strategies in exponential additive models.
result Provide necessary conditions for deriving expressions and confirm integrability conditions for specific models.
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.
Investigates optimal portfolios with risk-free assets, minimizing investment risk.
problem Investment risk minimization with budget and return constraints.
method Replica analysis and exploration of implications of a risk-free asset.
result Implications of a risk-free asset on optimal portfolio and investment risk.
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
Study dynamic hedging of credit risk using a new model.
problem Dynamic hedging of counterparty risk for credit derivatives.
method Empirically driven credit model with interacting default intensities; Galtchouk-Kunita-Watanabe decomposition; closed-form risk minimizing strategy.
result Closed-form representation for risk minimizing strategy in nonlinear recursive systems.
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.
Paper analyzes time series prediction using empirical risk minimization.
problem Optimizing 1-step-ahead prediction for time series.
method Empirical risk minimization applied to recursive algorithms for time series forecasting.
result Empirical risk minimization achieves optimal predictive performance.
Research shows minimal communication limits adaptive function estimation rates.
problem Adaptive estimation of a smooth function under minimal communication constraints.
method Investigates the L∞-risk and L2-risk under different numbers of servers. result For L∞-risk, optimal rates cannot be achieved under minimal communication. For L2-risk, adaptivity is possible but depends on server number and sample size. Algorithm minimizes risk for multiclass classification of stochastic diffusion paths.
problem Multiclass classification of stochastic diffusion paths with distinct drift functions.
method Empirical risk minimization using L2 risk.
result Achieves fast rates of convergence under margin assumption.
Study on estimating class probabilities using empirical risk minimization.
problem Estimating class probabilities within binary classification.
method Empirical risk minimization (ERM) for class probability estimation.
result The estimator converges to true class probabilities under certain conditions.
Paper analyzes mortality risk minimization with and without securitization.
problem Risk minimization in equity-linked mortality contracts with arbitrary death time.
method Optional martingale representation and enlarged filtration to consider death uncertainty.
result Quantifies the effect of mortality uncertainty on risk-minimizing strategies.
The study proposes a method for risk reduction without relying on risk measurement.
problem Theoretical utopia of risk minimization vs. practical risk reduction.
method Generalization of matrix rank and condition number for identifying riskiest scenarios.
result Risk reduction achieved without risk measurement, validated by real data.
This work addresses time inconsistency in risk measures and develops a dynamic programming principle for risk minimization problems.
problem Time inconsistency in optimized certainty equivalents (OCEs) risk measures.
method Enlargement of state space to achieve a substitute for time consistency, derivation of dynamic programming principle.
result Characterization of the value function via viscosity solutions of Hamilton--Jacobi--Bellman--Issacs equations.
Empirical risk minimizers can be non-monotonic in learning curves.
problem Understanding the behavior of learning curves for empirical risk minimizers.
method Introducing risk monotonicity and analyzing its implications for various learners.
result Standard learners that minimize empirical risk can be non-monotonic regardless of training sample size.
Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…
New method for valuing and hedging credit risk when defaults cannot be hedged.
problem Valuation and hedging of counterparty credit risk when there's no protection available.
method Local risk-minimization approach via BSDE (Backward Stochastic Differential Equation)
result Optimal strategy computed for valuing and hedging credit risk.
The paper analyzes risk bounds and Rademacher complexity in batch RL.
problem Estimating/minimizing Bellman error with general value function approximation.
method Characterizes generalization performance using Rademacher complexities of function classes.
result Risk bounds and Rademacher complexities provide insights into batch RL.
The paper tackles fairness in machine learning by incorporating it into empirical risk minimization.
problem Ensuring fairness in classifier outcomes by preventing sensitive variables from unfairly influencing results.
method Empirical risk minimization with a fairness constraint that maintains approximately constant conditional risk with respect to the sensitive variable.
result The approach is statistically consistent and can be applied to kernel methods and linear models with simple preprocessing steps.
In this paper, we investigate risk minimization problem of derivatives based on non-tradable underlyings by means of dynamic g-expectations which are slight different from conditional g-expectations. In this framework, inspired by [1] and [16], we introduce risk indifference price, marginal risk price and derivative he…
New framework for conditional risk minimization using optimal transport.
problem High-stakes decisions with side information, especially economic conditions.
method Universal framework based on union-ball formulation in optimal transport.
result Offers interpretability, tractability, and scalability for various risk functionals.
Bayesian optimization reduces CVaR portfolio risk.
problem Minimizing CVaR under minimum expected return constraints.
method New Bayesian Optimization algorithms with a two-stage procedure.
result Significant reduction in objective function evaluations.
Optimizes investment risk with cost using replica analysis.
problem Minimizing investment risk with cost.
method Replica analysis of Hamiltonians in mean-variance model.
result Derives minimal investment risk with cost and optimal portfolio investment concentration.
Improved sample complexity for diffusion models without needing empirical risk minimizers.
problem Theoretical limitations in sample complexity for diffusion models.
method Structured decomposition of score estimation error, eliminating dependence on neural network parameters.
result Achieved sample complexity bound of O(ε^(-4)) without empirical risk minimizer access.
Solves empirical risk minimization for relational data using graph sampling.
problem Empirical risk minimization for relational data.
method Graph sampling theory, stochastic gradient descent, automatic differentiation.
result Automatic unbiased stochastic gradients for relational data.