For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is a process with independent increments (PII) and an exponential of a PII process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to mo…
A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exact…
In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
Closed pricing formulas for Variance Gamma model payoffs.
problem Pricing path-independent payoffs in the Variance Gamma model.
method Mellin transform theory and multidimensional complex analysis.
result Closed-form pricing formulas with accelerated convergence for short-term options.
Introduce a variance-weighted batch distribution for diverse sampling in diffusion models.
problem Independent sampling in diffusion models.
method Introduce a variance-weighted batch distribution.
result Sampler with a transparent probabilistic target.
Study ridge regression for non-identically distributed data with varying variances.
problem Investigate high-dimensional regression with non-identical data variance.
method Propose a random effect model and use tools from random matrix theory.
result Highlight the double descent phenomenon in high-dimensional regression for certain variance profiles.
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
The paper shows how shared random seeds can reduce variance in machine learning evaluations.
problem The statistical structure of comparative evaluation under shared random seeds is not well understood.
method An extended learning-based multi-agent economic simulator was used to demonstrate the effects of shared random seeds on variance reduction.
result Pairing seeds can reduce variance in machine learning evaluations, especially when outcomes are positively correlated at the seed level.
Faster convergence of kernel mean embeddings using variance information.
problem Speeding up the convergence rate of kernel mean embeddings.
method Leveraging variance information in reproducing kernel Hilbert space and estimating variance from data.
result Efficiently estimate variance information from data to achieve distribution-agnostic convergence bounds.
Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang we showed that a…
New method improves convergence and reduces variance in noisy optimization problems.
problem Computing exact minimizers with noisy gradient information.
method Stochastic mirror descent with interacting particles.
result Interaction helps improve convergence and reduce variance.
New methods infer causal structure from data without hidden variables.
problem Inferring causal structure from observational data with hidden variables.
method Introduces alternative independence tests and conditionally-additive-noise models.
result Can infer causal relations without assumptions about equation form or hidden variables.
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over input dependent noise variance (heteroscedasticity) and input dependent signal varia…
We consider a square-integrable semimartingale and investigate the convex order relations between its discrete, continuous and predictable quadratic variation. As the main results, we show that if the semimartingale has conditionally independent increments and symmetric jump measure, then its discrete realized variance…
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this cla…
Paper tackles unknown variances in best-arm identification.
problem Identifying the best arm with unknown variances in Gaussian distributions.
method Two approaches: empirical variance plugging or adapting transportation costs.
result The impact of unknown variances is small on sample complexity.
Optimizes embedding accuracy for data variance and error.
problem Efficiently embedding data while minimizing distortion.
method Uses Johnson-Lindenstrauss embeddings with orthogonal matrices and singular-value latent variables.
result Achieves best accuracy in variance, mean-squared error, and length distortion.
Proposes SVI for covariate-shift generalization with sparse variable independence.
problem Covariate-shift generalization with limited data and unstable variables.
method Introduces sparsity constraint and combines reweighting and selection in an iterative way.
result Improves covariate-shift generalization performance on synthetic and real-world datasets.
Sharp inequalities for matrix means with unknown variance.
problem Estimating matrix means with unknown variance.
method Empirical Bernstein inequalities for symmetric random matrices.
result Adapts to unknown variance with tight deviation bounds.
Bayesian method recovers causal structure in SEMs with equal error variances.
problem Recovering causal structure in SEMs with equal error variances.
method Bayesian DAG selection method using g-priors and the key property of minimum expected squared errors.
result The method consistently recovers the true graph without additional distributional assumptions.
We consider the discretized version of a (continuous-time) two-factor model introduced by Benth and coauthors for the electricity markets. For this model, the underlying is the exponent of a sum of independent random variables. We provide and test an algorithm, which is based on the celebrated Foellmer-Schweizer decomp…
This paper extends the MAB problem to consider risk-reward tradeoffs.
problem Maximizing reward while accounting for risk in multi-armed bandit problems.
method Introduced the Risk Aware Lower Confidence Bound (RALCB) algorithm to solve the mean-variance MAB problem.
result The RALCB algorithm performs better than the algorithm in Sani et al. (2012) in both independent and dependent scenarios.
New estimator reduces bias and variance issues in mutual information estimation.
problem Difficulty in using variational MI estimators due to bias/variance tradeoffs and self-consistency issues.
method Developed a new estimator based on a unified perspective of variational approaches, focusing on variance reduction.
result Empirical results show improved bias-variance trade-offs compared to existing estimators.
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t…
Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…
New algorithms reduce regret in both stochastic and deterministic environments.
problem Designing algorithms that perform well in both types of MDPs.
method Proposed new environment norms and algorithms with variance-dependent regret bounds.
result First algorithm with simultaneously optimal bounds for both stochastic and deterministic MDPs.
Alternative to likelihood-based LSNM model selection, residual independence testing is more robust to noise misspecification.
problem Cause-effect inference in location-scale noise models with misspecified noise distributions.
method Residual independence testing as an alternative to likelihood-based model selection.
result Residual independence testing is more robust to noise misspecification.
Improved CountSketch method reduces variance for estimating vector coordinates.
problem Estimating coordinates of high-dimensional vectors efficiently.
method Revisits CountSketch method, using median of estimates to reduce variance.
result Variance reduced to O(min{∥v∥12/s2,∥v∥22/s}) for t>1. Improved PAC-Bayesian bounds by considering example difficulty.
problem Improving generalization bounds in machine learning.
method Introducing a modified excess risk that leverages example difficulty to reduce variance and tighten PAC-Bayesian bounds.
result Tighter PAC-Bayesian generalization bounds for machine learning models.
Proposes a modified Morgan-Pitman test for evaluating variances in machine learning models.
problem Limited ability to account for sampling variability in model selection.
method Enhances the classic Morgan-Pitman test for robustness in non-linear models with heavy-tailed distributions or outliers.
result Demonstrates the test's effectiveness and practical utility in model evaluation and selection.
We solve the paradox of score-based methods by minimizing path variance.
problem Score-based methods are path-dependent, leading to inaccurate and unstable estimators.
method Propose MVP Principle to minimize path variance, derive closed-form expression, and use flexible Kumaraswamy Mixture Model.
result Establishes new state-of-the-art results on challenging benchmarks.
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by Lévy processes, extending earlier works which focused on the Black-Scholes and continuous stochastic volatility models. Usin…
New model for pricing volatility derivatives considering rough volatility and jumps.
problem Modeling instantaneous volatility with rough volatility and jumps.
method Generalized fractional Ornstein-Uhlenbeck process with Lévy subordinator and sinusoidal-composite Lévy process.
result Pricing-hedging formulae for power-type derivatives on average forward variance are derived.
The paper characterizes optimal dynamic portfolios for a modified mean-variance utility.
problem Optimal dynamic portfolio choice for a modified mean-variance utility.
method Complete characterization under minimal assumptions, no restrictions on asset return moments.
result Maximal MMV utility is linked to the monotone Sharpe ratio, with global squared MSR as the nominal yield.
Machine learning reduces variance in online experiment results.
problem Reducing variance in randomized controlled trials.
method Machine learning regression-adjusted treatment effect estimator (MLRATE).
result MLRATE reduces estimator variance by over 70% in A/A tests.
Integrates prediction models into portfolio optimization for better asset allocation.
problem Traditional portfolio optimization ignores prediction models, leading to suboptimal decisions.
method Developed a framework that combines regression prediction with mean-variance optimization, providing analytical solutions and neural-network-based optimization for inequality constraints.
result Demonstrated through simulations that integrating prediction models improves portfolio performance.
SkMM selects data for finetuning by balancing bias and variance.
problem Balancing bias and variance in high-dimensional finetuning.
method Gradient sketching for bias reduction and moment matching for variance reduction.
result Gradient sketching selects samples efficiently and accurately.
VRCQ algorithm reduces variance in Q-learning for MDPs, achieving optimal sample complexity.
problem Estimating the optimal Q-function in MDPs with synchronous sampling.
method VRCQ combines direct variance reduction and Cascade Q-learning.
result VRCQ is minimax optimal and instance optimal for single-action problems.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
Improves diffusion models by controlling total variance and signal-to-noise-ratio.
problem Long sampling time in diffusion models.
method Total-Variance/Signal-to-Noise-Ratio (TV/SNR) disentangled framework.
result Improves generation performance by controlling TV and SNR independently.
Paper improves CMAB regret bounds by reducing batch-size dependency.
problem Reducing batch-size dependency in combinatorial semi-bandits.
method Developed BCUCB-T and SESCB algorithms with new TPVM conditions.
result Significantly improved regret bounds for various applications.
Stochastic optimization techniques are standard in variational inference algorithms. These methods estimate gradients by approximating expectations with independent Monte Carlo samples. In this paper, we explore a technique that uses correlated, but more representative , samples to reduce estimator variance. Specifical…
Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root's work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding p…
Polynomial-time algorithm learns causal graphs without parametric assumptions.
problem Learning causal graphs from data without assuming linearity or parametric forms.
method Model-free polynomial-time algorithm with finite-sample guarantees.
result Algorithm achieves linear cost in dimension and samples compared to optimal.
We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that the mean realized variance of returns is a linear function of the number of day…
BBVI converges nearly dimensionally independent for log-concave targets.
problem Efficiently optimizing variational parameters in high-dimensional spaces.
method Proved convergence rate of BBVI with reparametrization gradient for log-concave targets.
result BBVI converges with nearly independent dimension dependence for log-concave targets.
Paper improves sparse linear bandits by accounting for noise variance.
problem Sparse linear bandits with unknown noise variance.
method Develops a general framework to convert variance-aware algorithms to sparse linear bandits.
result Achieves $\widetilde{\mathcal O}\left(\sqrt{d\sum_{t=1}^T σ_t^2} + 1
ight)$ regret, interpolating between worst-case and benign settings.
Estimates variance function using aggregation methods in regression models.
problem Estimating variance function in regression models.
method Two-step procedure involving model selection or convex aggregation, using two independent samples.
result Consistency of the proposed method in L2 error for MS and C aggregations.