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 “Local risk-minimization”
Study local risk-minimizing strategies for Barndorff-Nielsen and Shephard models.
problem Develop strategies for minimizing risk in financial markets with stochastic volatility.
method Apply Malliavin calculus for Levy processes to derive formulas for risk-minimizing strategies.
result Explicit representations of risk-minimizing strategies for call and put options in Barndorff-Nielsen and Shephard models.
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.
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]
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.
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.
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.
Local risk-minimization for Barndorff-Nielsen and Shephard models with volatility risk premiumq-fin.MF
Paper analyzes call and put options for jump type stochastic volatility models with volatility risk premium.
problem Local risk-minimization for call and put options in Barndorff-Nielsen and Shephard models with volatility risk premium.
method Derives representations using Malliavin calculus under the minimal martingale measure.
result Relaxes the constraint on volatility risk premium and restricts leverage effect to .
In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of in…
Enhanced Gordon growth model for valuing financial products.
problem Valuation of financial products with time-varying interest rates and dividends.
method Dynamic Gordon growth model with time-varying spot interest rate and dividends, risk-neutral valuation, locally risk-minimizing strategy.
result Pricing and hedging formulas for dividend-paying European options and equity-linked life insurance products.
Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard modelsq-fin.CP
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
problem Calculating locally risk-minimizing strategies for non-martingale BNS models with infinite active jumps.
method Modified Malliavin calculus expression and Monte Carlo method for non-martingale BNS models.
result Proposes a numerical method for LRM strategies in non-martingale BNS models with infinite active jumps.
We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure …
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.
Optimizes exp-concave losses with a new risk bound.
problem Optimizing exp-concave losses with stochastic convex optimization.
method Empirical Risk Minimization with a unified geometric assumption and local norms.
result Provides an excess risk bound.
In this paper we investigate the local risk-minimization approach for a semimartingale financial market where there are restrictions on the available information to agents who can observe at least the asset prices. We characterize the optimal strategy in terms of suitable decompositions of a given contingent claim, wit…
Paper addresses ERM in non-interactive local differential privacy, reducing sample complexity in high dimensions.
problem Empirical Risk Minimization in non-interactive local differential privacy with high dimensionality.
method Polynomial approximation for constant or low dimensionality, 1-bit communication for high dimensionality.
result Achieves error bounds independent of dimensionality for constant or low dimensionality, dependent on Gaussian width for high dimensionality.
On Acceleration of Gradient-Based Empirical Risk Minimization using Local Polynomial Regressionmath.OC
Accelerates ERM problems with LPI-GD and improved oracle complexity.
problem Empirical Risk Minimization (ERM) problems with strong convexity and smoothness.
method Local Polynomial Interpolation-based Gradient Descent (LPI-GD) and accelerated methods.
result Oracle complexity improved to $ ilde{O}\left(\sqrtσ m^d \log(1/\varepsilon)
ight)$.
Improved ADMM for convex distributed learning with differential privacy.
problem Privacy concerns in distributed learning with sensitive data.
method Approximate multi-step ADMM with calibrated noise.
result Higher utility and error bounds asymptotic to state-of-the-art.
The paper analyzes local minima in high-dimensional empirical risk minimization.
problem Understanding local minima in high-dimensional data models.
method Using Kac-Rice formula and proportional asymptotics, the paper derives bounds on local minima.
result Sharp asymptotics on estimation and prediction errors are derived.
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.
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.
This guide simplifies high-probability regret bounds in empirical risk minimization.
problem High-probability regret bounds in empirical risk minimization.
method Modular presentation, three-step recipe, localized Rademacher complexity, local maximal inequalities, metric-entropy integrals.
result Recover familiar rates for various function classes and derive regret bounds for nuisance components.
ERM and RERM minimize error even with malicious label corruptions.
problem Malicious label corruptions in regression problems.
method Empirical Risk Minimizers (ERM) and Regularized Empirical Risk Minimizers (RERM) under a local Bernstein condition.
result The -error rate is bounded by $r_N + AL |\cO|/N$ under the local Bernstein condition.
Paper addresses ERM in LDP, reducing sample complexity for smooth and convex losses.
problem Achieving error α in ERM with non-interactive LDP, especially for high-dimensional data.
method Developed algorithms using Bernstein polynomial and polynomial approximation techniques.
result For smooth and convex losses, sample complexity is linear in dimensionality.
Sharp bounds on ERM's minimal error in regression.
problem Understanding ERM's performance in regression tasks.
method Sharp lower bounds for ERM in random and fixed design settings.
result ERM's performance depends on the global or local complexity of the model.
Analyzes how learning algorithms affect and are affected by data manipulation.
problem Characterizing the closed-loop behavior of learning algorithms in the presence of decision-dependent data.
method Analyzes repeated risk minimization as perturbed gradient flows of performative risk minimization, considering multiple local minimizers.
result Characterizes the region of attraction for various equilibria and introduces performative alignment.
Study shows neural network parameters converge to ridgelet spectrum.
problem Characterization of local minima in over-parametrized neural networks.
method Developed ridgelet transform to analyze neural network parameters.
result Distribution of parameters converges to ridgelet spectrum.
The paper provides VIX option pricing and hedging strategies for two stochastic volatility models.
problem Pricing and hedging of VIX options for specific stochastic volatility models.
method Develops representations of VIX call option prices and locally risk-minimizing strategies for Barndorff-Nielsen and Shephard models.
result Efficient representations and locally risk-minimizing strategies for numerical methods.
GIANT optimizes distributed computing by improving Newton method efficiency.
problem Efficiently solving empirical risk minimization problems in distributed environments.
method GIANT combines local ANT directions to form a GIANT direction, averaging communications and computations.
result GIANT achieves faster convergence compared to first-order and existing Newton-type methods.
We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal m…
Max-diversity improves distributed learning performance.
problem Improving risk performance in distributed learning.
method Max-diversity distributed learning algorithm (MDD).
result MDD outperforms existing methods with tighter risk bounds.
Paper introduces input perturbation for privacy in machine learning models.
problem Protecting both training data and model parameters while maintaining privacy.
method Add noise to training data and train with perturbed data for differential privacy.
result Achieves (ε,δ)-differential privacy on the final model with privacy on original data.
This work characterizes optimal multiclass learning with regularization.
problem The empirical risk minimization (ERM) algorithm fails in multiclass learning settings.
method Using one-inclusion graphs (OIGs), the work introduces optimal learning algorithms that relax structural risk minimization and incorporate unsupervised learning.
result An optimal learner is introduced that uses a local regularization function and an unsupervised learning stage to learn the regularizer.
New algorithm improves gradient-based ERM for smooth convex losses.
problem Empirical risk minimization of smooth, strongly convex loss functions.
method Iterative gradient-based method with local polynomial regression.
result Oracle complexity of for our algorithm.
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.
The paper addresses convergence of option price estimation in a regime-switching market.
problem Estimating the transition rate of regime switching in a market.
method Approximating the transition rate estimator in smooth functions and proving convergence of the option price.
result Point-wise convergence of the approximated option price, verifying its applicability in finance.
Paper proves well-posedness of PDE for option pricing in a complex market model.
problem Derivative pricing in a generalized market model with non-local parabolic PDE.
method Used Volterra integral equation and probabilistic approach with conditioning on stopping times.
result Proved well-posedness of the initial-boundary value problem for the PDE.
Localized SVMs maintain SVM's consistency properties for large datasets.
problem Inefficient computational requirements of global SVMs for large data sets.
method Localized SVMs apply different hyperparameters to different regions of the input space.
result Localized SVMs inherit - and risk consistency from global SVMs.
Empirical Risk Minimization in the Interpolating Regime with Application to Neural Network Learningstat.ML
New insights into neural network training show some interpolating methods can generalize well, while others fail catastrophically.
problem Understanding why neural networks trained to interpolate can still generalize well or fail catastrophically.
method Analyzing empirical risk minimization (ERM) over large hypotheses classes, focusing on interpolating methods.
result Some interpolating ERM-like methods for large hypotheses classes provide good statistical guarantees, while others fail catastrophically.
We analyze the landscape of empirical risk minimization for high-dimensional models, predicting phase transitions and critical point properties.
problem Understanding the complexity and structure of high-dimensional empirical risk landscapes.
method Using the Kac-Rice formula, we analyze the expected number of critical points and their spectral properties, providing detailed predictions.
result We derive complete topological phase diagrams for the phase retrieval problem, predicting BBP-type transitions and critical point stability.
Local regularization fails in transductive learning for some multiclass problems.
problem Whether local regularization can learn all transductive multiclass problems.
method Provided a negative answer by exhibiting a specific multiclass problem.
result Local regularization cannot learn all transductive multiclass problems.
This work models overnight rates with jumps and discontinuities, extending classical short-rate models.
problem Capturing the jump behavior and discontinuities in overnight rates for accurate modeling.
method Developed a term structure modeling framework based on overnight rates, accommodating stochastic discontinuities.
result Simple specifications can capture the jump behavior of overnight rates, and explicit valuation formulas are provided.
Privacy Aware Learningstat.ML
We study statistical risk minimization problems under a privacy model in which the data is kept confidential even from the learner. In this local privacy framework, we establish sharp upper and lower bounds on the convergence rates of statistical estimation procedures. As a consequence, we exhibit a precise tradeoff be…