This work proposes using zero-variance control variates to reduce variance in pathwise gradient estimators for variational inference.
problem Pathwise gradient estimators in variational inference have high variance, leading to inefficient optimization.
method Apply zero-variance control variates to pathwise gradient estimators.
result Zero-variance control variates can significantly reduce the variance of pathwise gradient estimators without requiring complex assumptions.
A new approach to continuous-time universal portfolios using pathwise Itô calculus.
problem Continuous-time version of Cover's universal portfolio strategies.
method Pathwise Itô calculus approach to establish existence and properties of universal portfolio strategies.
result The universal portfolio strategy's portfolio value process is the average of all values of constant rebalanced strategies.
Develops pathwise analysis for log-optimal portfolios using rough paths theory.
problem Analyzing stability and approximation of log-optimal portfolios.
method Pathwise approach based on càdlàg rough paths theory.
result Establishes pathwise stability and error estimates for log-optimal portfolios.
New Monte Carlo method for calculating sensitivities of barrier options.
problem Calculating sensitivities for discontinuous payoff functions in barrier options.
method Combining one-step survival idea with stable differentiation approach.
result Calculated sensitivities for different types of barrier options.
Develops portfolio theory without probabilistic analysis, focusing on pathwise decomposition.
problem Ensuring market viability without probabilistic assumptions.
method Uses pathwise decomposition and trend extractors to replace semimartingale decomposition.
result Growth-numéraire and viability equivalences are similar but not identical in pathwise setting.
We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are d-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategie…
This paper develops a mathematical framework for the analysis of continuous-time trading strategies which, in contrast to the classical setting of continuous-time mathematical finance, does not rely on stochastic integrals or other probabilistic notions. Our purely analytic framework allows for the derivation of a path…
Pathwise uniqueness shown for specific stochastic equations.
problem Stochastic Volterra equations with singular kernels and Hölder coefficients.
method Established pathwise uniqueness through Hölder continuity of coefficients.
result Pathwise uniqueness and existence of unique strong solutions.
A new method in finance without probabilities or integrals.
problem Creating a model-free approach to continuous-time finance.
method Pathwise approach using causal functional calculus and transition principle of Isaacs.
result A fully non-linear path-dependent equation characterizes optimal solutions.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
This work introduces efficient sampling methods for Gaussian processes by focusing on pathwise conditioning.
problem Intractable mathematical expressions in Gaussian process posteriors limit practical applications.
method Investigates a pathwise interpretation of conditioning to derive efficient sampling methods.
result Derives a general family of approximations that allow for efficient sampling of Gaussian process posteriors.
Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in those one-dimensional paths which do not possess local times. The local time is constructed from discrete approximations, and it is shown that it is α-Hölder …
Efficient pathwise gradient estimators for multivariate distributions.
problem Constructing efficient gradient estimators for multivariate distributions.
method Using null solutions of the transport equation and control variates for gradient estimation.
result Pathwise gradient estimators for mixtures of multivariate Normal distributions can outperform other methods in high dimensions.
New method computes pathwise gradients for non-reparameterizable distributions.
problem Computing gradients for complex distributions not directly amenable to the reparameterization trick.
method Using optimal transport theory, compute gradients for Gamma, Beta, and Dirichlet distributions.
result Optimal gradients have reduced variance and are competitive with other methods.
Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.
problem Estimating smooth Hilbert-valued parameters with theoretical guarantees.
method Pathwise differentiable Hilbert-valued parameters, efficient influence functions, regularized one-step estimators.
result Theoretical guarantees for efficient estimators even when nuisance functions are arbitrary.
The pathwise coordinate optimization is one of the most important computational frameworks for high dimensional convex and nonconvex sparse learning problems. It differs from the classical coordinate optimization algorithms in three salient features: {\it warm start initialization}, {\it active set updating}, and {\it …
The paper optimizes bridge-type estimators for sparse models using pathwise methods.
problem Sparse parametric models with adaptive coefficients and multiple penalties.
method Pathwise optimization with accelerated proximal gradient descent and blockwise alternating optimization.
result Efficient computation of the full solution path for adaptive bridge estimators.
We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô calculus and works for portfolios generated from functions that may depend on the current states of the market port…
Unified approach to financial market modeling in discrete time.
problem Establishing equivalence between pathwise and quasi-sure approaches.
method Unified framework proving Fundamental and Superhedging Theorems.
result Unified approach encompasses and clarifies different notions of arbitrage.
A scalable method for BED with implicit models using approximate gradients.
problem Efficiently estimating posterior distribution and maximizing MI for implicit models.
method Stochastic approximate gradient ascent with smoothed variational MI estimator.
result Significantly improves scalability of BED in high-dimensional problems.
We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including additivity boil down to invariances of the covariance kernel. These results are extended…
This paper simplifies hedge ratios in financial models using pathwise algorithmic differentiation.
problem Expensive and unstable computation of hedge ratios from pathwise sensitivities.
method Develops reduced stochastic hedge ratios of the form φ_j^r = Σ_j^r ξ_j^q X_q, retaining sensitivity tensor through empirical averages.
result Two coefficient criteria are introduced to minimize pathwise residuals and satisfy moment equations.
Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.
problem Computational challenges in high-dimensional ℓ1 penalized quantile regression. method Pathwise coordinate descent algorithm to solve exact coordinatewise minimum of the nonsmooth loss function.
result Algorithm runs faster than existing alternatives and maintains estimation accuracy.
This paper gives several simple constructions of the pathwise Ito integral ∫0tφdω for an integrand φ and a price path ω as integrator, with φ and ω satisfying various topological and analytical conditions. The definitions are purely pathwise in that neither φ nor ω are assumed to be paths of stochast…
New models avoid probability in option pricing, matching historical and implied volatilities.
problem Developing option pricing models without probability.
method Statistical analysis of historical volatility and pathwise lift of stock dynamics.
result Option pricing models can be based on pathwise properties of stock dynamics.
This dissertation advances scalable Gaussian processes using iterative methods and pathwise conditioning.
problem The classical Gaussian process formulation is not scalable for large datasets and modern hardware.
method Combining iterative methods and pathwise conditioning to improve scalability.
result Significantly reduced memory requirements and facilitated application to larger datasets.
MuRiT efficiently computes multi-parameter persistence barcodes.
problem Efficient computation of multi-parameter persistent homology.
method Vietoris-Rips transformation to reduce multi-parameter to single-parameter computation.
result MuRiT computes pathwise persistence barcodes for multi-filtered flag complexes.
We study the use of the multilevel Monte Carlo technique in the context of the calculation of Greeks. The pathwise sensitivity analysis differentiates the path evolution and reduces the payoff's smoothness. This leads to new challenges: the inapplicability of pathwise sensitivities to non-Lipschitz payoffs often makes …
Develops a new model-free approach to portfolio theory using rough paths.
problem Handles more general portfolios without probabilistic assumptions.
method Rough path theory for stochastic portfolio theory (SPT).
result Asymptotic growth rates of various portfolios match.
We consider a class X of continuous functions on [0,1] that is of interest from two different perspectives. First, it is closely related to sets of functions that have been studied as generalizations of the Takagi function. Second, each function in X admits a linear pathwise quadratic variatio…
The paper offers a pricing-hedging method for prediction sets.
problem Model-independent superhedging with pathwise constraints.
method Pathwise superhedging on prediction sets with respect to martingale measures.
result The superhedging price equals the supremum of pricing functionals over measures concentrated on the prediction set.
A new method for pricing and hedging options without using probability theory.
problem Pricing and hedging financial options using traditional probability methods.
method Using rough paths to encode volatility and enhance price trajectories for pathwise replication.
result A robust hedging strategy that is less sensitive to model misspecification.
Study shows how market firm capitalization models converge to stochastic PDE solutions.
problem Understanding convergence of rank-based models with common noise to stochastic PDE solutions.
method Analysis of mean field limit, martingale problem, and pathwise entropy solutions.
result Empirical cumulative distribution function converges to solution of a stochastic PDE under certain conditions.
NM-PPG optimizes adaptive feature acquisition in POMDPs for better predictions.
problem Optimizing adaptive feature acquisition in prediction problems with costly features.
method Non-myopic pathwise policy gradients (NM-PPG) with continuous relaxation and straight-through rollout.
result NM-PPG outperforms state-of-the-art AFA methods on synthetic and real-world datasets.
Exact simulation method for market impact estimation under various execution strategies.
problem Estimating market impact from observed price trajectories under different execution strategies.
method Conditional simulation of point processes under perturbed intensities.
result Exact, event-driven algorithm for reconstructing counterfactual paths.
A new reinforcement learning method uses model derivatives to improve policy optimization.
problem Improving sample efficiency and performance in model-based reinforcement learning.
method Constructs an actor-critic algorithm that uses the pathwise derivative of the learned model and policy.
result Consistently more sample efficient and matches model-free algorithms' asymptotic performance.
This study simplifies rough Heston model's conditional density equation.
problem Analyzing rough volatility in financial models.
method Pathwise transformation and Fokker-Planck formulation of conditional density equation.
result Transformed equation yields deterministic PDE with path-dependent coefficients.
Method learns dynamics from noisy partial observations.
problem Reconstructing stochastic dynamical systems from indirect noisy data.
method Amortized path generation method for nonlinear stochastic filtering.
result Learned conditional path generator quantifies uncertainty.
New method reduces errors in pricing and sensitivities for discontinuous payoffs.
problem Errors in pricing and sensitivities for discontinuous payoffs in digital and barrier options.
method Alternative methods for estimating sensitivities, including likelihood ratio and hybrid methods.
result New methods substantially reduce test errors in prices and sensitivities.
Deep learning approximates Bermudan option exposures and future values.
problem Computing accurate expected and future exposures for high-dimensional Bermudan options.
method Neural network-based approach combining Deep Optimal Stopping and regression.
result Neural network approximations of pathwise option values are more accurate.
Method uses derivatives for dynamic index tracking and risk control.
problem Dynamic index tracking and risk exposure control using financial derivatives.
method Continuous-time diffusion framework, pathwise approach to construct dynamic portfolios of derivatives.
result Established a general tracking condition and derived a slippage process.
New method generates portfolios using market weights and past data.
problem Creating efficient trading strategies based on market weights.
method Pathwise generation of portfolios using market weights and past data.
result Improved conditions for outperforming the market over time.
Effective dimensionality reduction improves accuracy and reduces costs in estimating option Greeks.
problem Estimating Greeks for barrier and arithmetic average Asian options.
method Global sensitivity analysis, Chebyshev interpolation, conditional pathwise method, randomized Quasi Monte Carlo, Brownian bridge discretization, importance sampling.
result Reduced effective dimensionality enhances convergence rate and accuracy of randomized Quasi Monte Carlo integration.
Proposes a new method for estimating non-pathwise differentiable functional parameters.
problem Estimating dose-response curves for continuous exposure.
method Targeted Highly Adaptive Lasso (HAL) for non-pathwise differentiable functional parameters.
result The Targeted HAL-MLE achieves dimension-free rates up to log(n) factors and outperforms other methods in simulations.
We obtain bounds on the distribution of the maximum of a martingale with fixed marginals at finitely many intermediate times. The bounds are sharp and attained by a solution to n-marginal Skorokhod embedding problem in Obłój and Spoida [An iterated Azéma-Yor type embedding for finitely many marginals (2013) Preprint]…
We consider a class of discrete time stochastic control problems motivated by some financial applications. We use a pathwise stochastic control approach to provide a dual formulation of the problem. This enables us to develop a numerical technique for obtaining an estimate of the value function which improves on purely…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
problem Approximating functionals of non-geometric rough paths.
method Extending rough paths with time and quadratic variation terms, proving uniform approximation.
result Linear functionals of extended signatures uniformly approximate continuous functionals.