Rough kernel hedging

• URL: http://arxiv.org/abs/2501.09683v2
• Date: Wed, 05 Feb 2025 18:00:59 GMT
• Title: Rough kernel hedging
• Authors: Nicola Muca Cirone, Cristopher Salvi,
• Abstract summary: We propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach.
• Score: 4.272515397452792
• License:
• Abstract: Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging problems. We make minimal assumptions about market dynamics by modelling them as general geometric rough paths, yielding a fully model-free approach. Furthermore, through a representer theorem, we provide theoretical guarantees on the existence and uniqueness of a global minimum for the resulting optimization problem and derive an analytic solution under highly general loss functions. Similar to the popular deep hedging approach, but in a more rigorous fashion, our method can also incorporate additional features via the underlying operator-valued kernel, such as trading signals, news analytics, and past hedging decisions, closely aligning with true machine-learning practice.

Related papers

• Gradients can train reward models: An Empirical Risk Minimization Approach for Offline Inverse RL and Dynamic Discrete Choice Model [9.531082746970286]
  We study the problem of estimating Dynamic Choice (DDC) models, also known as offline Maximum Entropy-Regularized Inverse Reinforcement Learning ( offline MaxEnt-IRL) in machine learning. The objective is to recover reward or $Q*$ functions that govern agent behavior from offline behavior data. We propose a globally convergent gradient-based method for solving these problems without the restrictive assumption of linearly parameterized rewards.
  arXiv  Detail & Related papers  (2025-02-19T22:22:20Z)
• Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent [36.59087823764832]
  This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines. For classification problems, this approach allows us to learn bounded geometric structures around given data points.
  arXiv  Detail & Related papers  (2024-07-05T08:20:27Z)
• A Unified Theory of Stochastic Proximal Point Methods without Smoothness [52.30944052987393]
  Proximal point methods have attracted considerable interest owing to their numerical stability and robustness against imperfect tuning. This paper presents a comprehensive analysis of a broad range of variations of the proximal point method (SPPM)
  arXiv  Detail & Related papers  (2024-05-24T21:09:19Z)
• The Dynamics of Riemannian Robbins-Monro Algorithms [101.29301565229265]
  We propose a family of Riemannian algorithms generalizing and extending the seminal approximation framework of Robbins and Monro. Compared to their Euclidean counterparts, Riemannian algorithms are much less understood due to lack of a global linear structure on the manifold. We provide a general template of almost sure convergence results that mirrors and extends the existing theory for Euclidean Robbins-Monro schemes.
  arXiv  Detail & Related papers  (2022-06-14T12:30:11Z)
• Gradient Backpropagation Through Combinatorial Algorithms: Identity with Projection Works [20.324159725851235]
  A meaningful replacement for zero or undefined solvers is crucial for effective gradient-based learning. We propose a principled approach to exploit the geometry of the discrete solution space to treat the solver as a negative identity on the backward pass.
  arXiv  Detail & Related papers  (2022-05-30T16:17:09Z)
• Nonparametric learning of kernels in nonlocal operators [6.314604944530131]
  We provide a rigorous identifiability analysis and convergence study for the learning of kernels in nonlocal operators. We propose a nonparametric regression algorithm with a novel data adaptive RKHS Tikhonov regularization method based on the function space of identifiability.
  arXiv  Detail & Related papers  (2022-05-23T02:47:55Z)
• Optimal variance-reduced stochastic approximation in Banach spaces [114.8734960258221]
  We study the problem of estimating the fixed point of a contractive operator defined on a separable Banach space. We establish non-asymptotic bounds for both the operator defect and the estimation error.
  arXiv  Detail & Related papers  (2022-01-21T02:46:57Z)
• Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness [68.97830259849086]
  Most datasets only capture a simpler subproblem and likely suffer from spurious features. We study adversarial robustness - a local generalization property - to reveal hard, model-specific instances and spurious features. Unlike in other applications, where perturbation models are designed around subjective notions of imperceptibility, our perturbation models are efficient and sound. Surprisingly, with such perturbations, a sufficiently expressive neural solver does not suffer from the limitations of the accuracy-robustness trade-off common in supervised learning.
  arXiv  Detail & Related papers  (2021-10-21T07:28:11Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Polynomial-Time Exact MAP Inference on Discrete Models with Global Dependencies [83.05591911173332]
  junction tree algorithm is the most general solution for exact MAP inference with run-time guarantees. We propose a new graph transformation technique via node cloning which ensures a run-time for solving our target problem independently of the form of a corresponding clique tree.
  arXiv  Detail & Related papers  (2019-12-27T13:30:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.