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.
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 .
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.
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.
Paper proposes a new method for WDRO with local perturbations, achieving better accuracy.
problem Wasserstein distributionally robust optimization's theoretical understanding needs improvement.
method Develops a new approximation theorem and risk consistency results for WDRO.
result The proposed method achieves significantly higher accuracy on noisy datasets.
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.
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.
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 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.
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 …
Research shows minimal communication limits adaptive function estimation rates.
problem Adaptive estimation of a smooth function under minimal communication constraints.
method Investigates the -risk and -risk under different numbers of servers.
result For -risk, optimal rates cannot be achieved under minimal communication. For -risk, adaptivity is possible but depends on server number and sample size.
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…
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.
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.
Study examines insider trading in short-selling restricted markets.
problem Analyzing insider trading opportunities in short-selling prohibited markets.
method Introducing minimal supermartingale measure and analyzing its properties in relation to minimal martingale measure.
result Conditions under which both measures fail to exist, indicating insider information affecting market perception.
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…
AMP regularization improves deep learning models by favoring flat minima.
problem Improving deep learning model generalization and avoiding overfitting.
method AMP regularization uses adversarial model perturbation to minimize a norm-bounded perturbation of the empirical risk.
result AMP regularization leads to state-of-the-art performance across various deep architectures.
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.
SGLD algorithm analyzes hitting time to local minima in non-convex optimization.
problem Non-convex optimization problems in machine learning.
method Stochastic Gradient Langevin Dynamics with Gaussian noise injection.
result SGLD achieves approximate local minima of population risk in polynomial time.
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…
Modeling central bank strategy to minimize risk in pegged currency markets.
problem Maintaining a pegged currency market from speculative investor attacks.
method Mathematical modeling of a stochastic game between a trader and a central bank.
result Identifying the optimal strategy for the central bank to minimize risk.
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)$.
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.
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.
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.
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.
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.
Local risk-minimization with multiple assets under illiquidity with applications in energy marketsq-fin.MF
Proposes hedging strategy for energy markets with liquidity constraints.
problem Hedging contingent claims with liquidity constraints and transaction costs.
method Risk-minimization approach targeting tradeoff between price fluctuations and liquidity costs, using discrete-time analysis and supply curve models.
result Closed-form solution for optimal hedging strategy under stochastic liquidity risk.
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.
Using integration by parts on Gaussian space we construct a Stein Unbiased Risk Estimator (SURE) for the drift of Gaussian processes using their local and occupation times. By almost-sure minimization of the SURE risk of shrinkage estimators we derive an estimation and de-noising procedure for an input signal perturbed…
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.
Risk-Control Strategiesq-fin.RM
The paper evaluates dynamic hedging strategies for various financial products.
problem Pricing derivative products with dynamic hedging and issuer-tailored risk.
method Unified constrained discrete stochastic dynamic programming framework with sequential local minimizing strategies.
result Demonstrates flexibility of the unified framework through numerical examples.
New bounds for non-convex estimators without Bernstein condition.
problem Sharp excess risk bounds for non-convex and improper estimators.
method Exponential-tail local Rademacher complexity risk bounds with offset condition.
result Sharp bounds for non-convex and improper estimators without Bernstein condition.
The paper characterizes dynamic return and star-shaped risk measures via BSDEs.
problem Characterizing dynamic return and star-shaped risk measures.
method Characterization of star-shaped functionals and BSDEs.
result Existence of convex BSDEs with non-empty set of supersolutions.
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.
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.
We consider the optimization of active extension portfolios. For this purpose, the optimization problem is rewritten as a stochastic programming model and solved using a clever multi-start local search heuristic, which turns out to provide stable solutions. The heuristic solutions are compared to optimization results o…