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…
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48 results for “risk-minimizing”
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.
Hedging of defaultable claims in a structural model using a locally risk-minimizing approachq-fin.MF
A method for hedging defaultable claims using locally risk-minimizing in a structural model.
problem Hedging defaultable claims in a structural model with jumps and non-risk-neutral probabilities.
method Locally risk-minimizing approach in a structural model with finite variation Levy process.
result Derivation of Follmer-Schweizer decompositions for hedging.
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.
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.
The paper proves convex risk minimization selects a unique conditional probability model.
problem General conditional probability estimation in various settings.
method Convex risk minimization and empirical risk minimization.
result The unique conditional probability model is selected by convex risk minimization.
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…
Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Accesscs.LG
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.
Develops a convex surrogate for variance in risk minimization.
problem Balancing approximation and estimation error in optimization.
method Combines distributionally robust optimization and empirical likelihood.
result Shows faster convergence rates than empirical risk minimization.
The paper analyzes the performance of empirical risk minimization for -norm linear regression.
problem Empirical risk minimization on -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.
Paper extends chaining technique for empirical risk minimization bounds.
problem Empirical risk minimization with unbounded noise and estimates.
method Chaining technique applied to random design settings, proving excess risk bounds.
result Proves upper bounds for empirical risk minimization with sub-Gaussian or subexponential noise.
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.
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]
Discussion of "2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization" by V. Koltchinskii [arXiv:0708.0083]
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.
Proposes a new framework for learning image augmentations to improve classification performance.
problem Improving classification performance with a given class of predictors.
method Transformed Risk Minimization (TRM) framework that optimizes both predictive models and data transformations.
result Performance of TRM with SCALE algorithm compares favorably to prior methods on CIFAR10/100.
Invariant Risk Minimizationstat.ML
IRM learns representations invariant to training distributions for better generalization.
problem Learning generalizable models across different training distributions.
method IRM learns a data representation that remains consistent across multiple training distributions, ensuring an optimal classifier matches across them.
result IRM enables out-of-distribution generalization by learning invariant correlations.
Taylor Learningstat.ML
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.
Paper compares two hedging strategies for Lévy models.
problem Difference between locally risk-minimizing and delta hedging strategies.
method Model-independent upper estimations and numerical examples for two Lévy models.
result Upper estimations for the difference between strategies.
Statistical learning theory explains SVMs for data-driven decision making.
problem Decision making and model construction from data.
method Statistical learning theory, focusing on empirical and structural risk minimization.
result Support Vector Machines (SVMs) are a prominent implementation of structural risk minimization.
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 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.
Empirical study of IRMv1, an invariant risk minimization framework.
problem Learning predictors invariant to spurious correlations across different training environments.
method Extending ColoredMNIST experiment to various settings.
result IRMv1 performs better as spurious correlation varies more widely.
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.
New method for calculating forex options using LRM for Lévy models.
problem Calculating local risk minimization for forex options in Lévy models.
method Transformed representation of LRM into fast Fourier transform form.
result Validated the method on Merton jump-diffusion and variance gamma models.
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.
The MAPE is equivalent to weighted MAE and EMRM can still be consistent under certain conditions.
problem Using MAPE as a quality measure for regression models.
method Equivalence of MAPE and weighted MAE, and analysis of EMRM consistency.
result Empirical Risk Minimization can remain consistent with MAPE under certain assumptions.
The paper analyzes prediction error in nonstationary settings using weighted risk minimization.
problem Prediction under distribution drift and nonstationary conditions.
method General decomposition of excess risk into learning and drift terms, proving oracle inequalities under mixing conditions.
result Oracle inequalities for the learning error, providing bounds that hold uniformly over arbitrary weight classes.
New robust estimators for risk minimization in statistical models.
problem Robust estimation in statistical models, especially in heavy-tailed settings.
method Novel robust gradient descent approach for convex risk minimization.
result Proves robustness of estimators in general statistical models and specific cases.
New method estimates Schrödinger bridge potentials via empirical risk minimization.
problem Estimating Schrödinger bridge potentials from samples.
method Rewriting Schrödinger system as a fixed-point equation and estimating the potential via empirical risk minimization.
result Uniform concentration of empirical risk around population counterpart under sub-Gaussian assumptions.
The paper studies generalization bounds for VRM, a variant of ERM.
problem Understanding the generalization performance of VRM.
method Proves generalization bounds for VRM under specific conditions.
result Generalization performance of VRM depends on vicinal function choice and function class quality.
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.
Fast algorithm tackles nonsmooth optimization problems.
problem Nonsmooth optimization in risk minimization.
method Continuation algorithm for nonsmooth regularized risk minimization.
result Achieves fastest known rates of convergence for strongly convex and general convex problems.
Bayesian CRM improves offline learning from logged bandit data.
problem Offline learning from logged bandit feedback.
method PAC-Bayesian analysis for a new generalization bound, novel regularization technique.
result New technique outperforms standard regularization and is competitive with variance regularization.
STORM enables edge computing for empirical risk minimization.
problem Training models on edge devices for streaming data.
method Online sketching for empirical risk minimization.
result STORM can estimate least-squares objective accurately.
Optimizes bilevel empirical risk minimization with improved oracle calls.
problem Optimizing bilevel empirical risk minimization problems.
method Proposes a bilevel extension of the SARAH algorithm.
result Demonstrates improved oracle calls to achieve stationarity.
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.
New algorithms improve empirical risk minimization across various settings.
problem Minimizing sums of convex functions efficiently.
method Developed a family of accelerated stochastic algorithms based on proximal point algorithm.
result Improved running time for empirical risk minimization across a wide range of problem settings.
IRM fails to improve over standard methods in complex settings.
problem Learning invariant features for out-of-distribution generalization.
method Analysis of Invariant Risk Minimization (IRM) and related approaches under a general model.
result IRM can fail catastrophically in non-linear settings, even when test data are similar to training distribution.
A method for classification using pairwise similarities and unlabeled data.
problem Handling pairwise similarities and unlabeled data for classification.
method Empirical risk minimization approach to create an unbiased risk estimator.
result Derives an unbiased risk estimator for handling both similarities and unlabeled data.
PF-based FSO methods improve on SGD and IPM for large-scale empirical risk minimization.
problem Optimizing large-scale empirical risk minimization problems efficiently.
method Developed PF-based stochastic optimizers (PFSOs) based on FSO methods.
result PFSOs outperform SGD, vanilla IPM, and KF-type FSO methods in stability, speed, and flexibility.
This work analyzes IRM and ERM from sample complexity perspective, revealing different behaviors under various distribution shifts.
problem Choosing between IRM and ERM for OOD generalization.
method Sample complexity analysis comparing IRM and ERM under different data generation mechanisms.
result IRM is preferred over ERM for certain distribution shifts, leading to better OOD generalization.
The issue of constructing a risk minimizing hedge under an additional almost-surely type constraint on the shortfall profile is examined. Several classical risk minimizing problems are adapted to the new setting and solved. In particular, the bankruptcy threat of optimal strategies appearing in the classical risk minim…
Dual optimization connects ERM-fDR to normalization function.
problem Empirical risk minimization with f-divergence regularization.
method Dual formulation, Legendre-Fenchel transform, implicit function theorem, nonlinear ODE.
result Computational method to calculate normalization function efficiently.