Stochastic processes and financial applications

Derniers papiers

• Sample-Smooth Spaces: A Convenient Category for Differentiable Probabilistic Programming

  Patrick Forr\'e · 23 septembre 2026

  We introduce the category $\mathbf{SSS}$ of sample-smooth spaces over a mixed site. The test objects are the products $\Omega_n := \mathbb{R}^n \times \Omega$ of a Cartesian space with the universal Hilbert cube $\Omega$ carrying all universally measurable sets, and a space is a set with a family of…

• Continuous Delayed-Memory Stochastic Gradient Descent and Continuous-Time Reinforcement Learning from History of Astrophysical Time Series Studies

  Debartha Paul, Juncheng Yi · 21 septembre 2026

  Quasars are luminous objects in the universe that exhibit stochastic brightness variations encoding information about the supermassive black holes powering them, and modeling these variations from ground-based survey data time series, known as light curves, is a statistical challenge. This paper rev…

• The Bias of Nonlinear Two-Time-scale Stochastic Approximation under Constant Step-Sizes

  Djamel Rassem Lamouri, Dorian Baudry, Nicolas Gast · 18 septembre 2026

  Two-timescale stochastic approximation (TTSA) is a fundamental tool for analyzing coupled iterative algorithms in reinforcement learning, optimization, and stochastic control. However, finite-time guarantees for nonlinear two-timescale schemes remain difficult to obtain, especially under constant st…

• Stochastic Gradient Descent over P2

  Maria Oprea, Qin Li, Yunan Yang · 16 septembre 2026

  Stochastic gradient descent (SGD) admits diffusion approximations that replace the complicated randomness of stochastic gradients by Gaussian noise, providing a powerful tool for understanding its dynamics and long-time behavior. We investigate whether an analogous approximation principle holds for …

• On the Equivalence of Stochastic Control and Path Space Formulations for Schr\"odinger Bridges over Compact Connected Lie Groups

  Hamza Mahmood, Georgiy A. Bondar, Abhishek Halder, Adeel Akhtar · 15 septembre 2026

  We establish the equivalence between the stochastic optimal control and path space formulations of the Schr\"odinger bridge problem (SBP) for the kinematic equation on a compact connected Lie group. Using the geometric concepts of horizontal lift and stochastic anti-development, we derive a Girsanov…

• Second-Order Smooth Planning with Optimal-Transport Bellman Smoothing

  Tuan Dam · 9 septembre 2026

  Planning with a generative model aims to estimate the value of a state using as few simulator calls as possible. SmoothCruiser achieves problem-independent complexity $\widetilde O(\varepsilon^{-4})$ by exploiting the smoothness of the entropy-regularized Bellman backup, but its estimator is only fi…

• Correlated initialization of deep residual networks

  Felix Benning, Ivan Nourdin, Giovanni Peccati · 4 septembre 2026

  We study the large-depth behavior of residual networks whose weights are correlated across layers at initialization. Our results confirm and extend a conjecture of Marion et al. [2025], according to which correlated initializations should interpolate continuously between the Brownian stochastic diff…

• Any-Order GPT as Masked Diffusion Model: Decoupling Formulation and Architecture

  Shuchen Xue, Tianyu Xie, Tianyang Hu, Zijin Feng, Jiacheng Sun, Kenji Kawaguchi, Zhenguo Li, Zhi-Ming Ma · 2 septembre 2026

  Efficiently scaling Large Language Models (LLMs) necessitates exploring alternatives to dominant autoregressive (AR) methods, with Masked Diffusion Models (MDMs) emerging as candidates. However, comparing AR (typically decoder-only) and MDM (often encoder-only) paradigms is confounded by differing a…

• Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces

  Jing Wang, Shuaiqiang Liu, Cornelis Vuik · 2 septembre 2026

  Generative models for implied volatility surfaces must produce outputs that satisfy static no-arbitrage constraints. We study these constraints in latent space. For a fixed generator, we assign each latent code a scalar margin determined by the no-arbitrage conditions of the generated surface. The c…

• Deep-MKV-TS: Path-Dependent McKean--Vlasov Control for Financial Time Series Generation

  Samer El Boustany, Th\'eo Basseras, Samy Mekkaoui, Alexandre Alouadi, Yadh Hafsi, Huy\^en Pham · 21 août 2026

  We introduce Deep-MKV-TS, a path-dependent McKean-Vlasov framework for financial scenario generation. The stochastic dynamics are chosen by matching selected path and volatility features of generated scenarios to those observed in the data. Starting from an interpretable reference model, Deep-MKV-TS…

• Variation Brownian Kernel Ladders

  Mahdi Mohammadigohari · 17 août 2026

  Claims about the benefit of depth depend on the complexity assigned to a representation. We introduce the \emph{Variation Brownian Kernel Ladder} (VBKL), a path-atomic function-space framework that separates nonlinear recursive dictionary construction from linear variation superposition. Starting fr…

• Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

  Konrad Kleinberg, Thomas Kruse · 11 août 2026

  In this paper we provide Monte Carlo and deep neural network approximations for stochastic representations of solutions to linear elliptic partial differential equations with constant diffusion, drift and killing. Building on the modified Walk-on-Spheres algorithm of Beznea et al. (arXiv:2209.01432)…

• A cylindrical neural approximation theorem for conditional laws of McKean-Vlasov equations with common noise

  Nacira Agram, Reda Hmioui, Jan Rems · 11 août 2026

  We introduce conditional cylindrical neural networks for approximating functionals of conditional laws in McKean-Vlasov equations with common noise. Fourier moments of the initial law and truncated signatures of the time augmented common noise are mapped by a mixture density network to a Gaussian mi…

• Neural Networks with Local Converging Inputs for Efficient Options Pricing Models

  Harris Cobb, Wenbo Hao, Yingjie Liu · 5 août 2026

  We present a novel application of Neural Networks with Local Converging Inputs (NNLCI) to improve the efficiency of existing numerical methods for pricing multi-asset options. The most concise input format for NNLCI has been introduced, offering substantial convenience and efficiency. NNLCI uses a n…

• Conditional Deep Levy Models for Exotic Derivatives: History-Aware Path Generation and P-Q Payoff Diagnostics

  Helin Zhao, Junchi Shen · 4 août 2026

  We develop and audit a history-aware financial path generator based on Denoising Levy Probabilistic Models (DLPMs) for conditional equity-index path generation. The model combines symmetric alpha-stable diffusion noise with a conditional U-Net observing the contract state, 60- and 252-day return his…

• Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility

  Xiaozhen Wang, Ana\"is Despr\'es, Martin Dureau, Francois Buet-Golfouse · 4 août 2026

  Local-stochastic volatility (LSV) combines vanilla marginals with richer smile dynamics, but calibration requires a slow, noisy and sequential McKean--Vlasov fixed point. We learn a projection-consistent operator for the calibration triple. Given finite quotes and a stochastic-volatility (SV) backbo…

• Learning Controlled Stochastic Differential Equations

  Luc Brogat-Motte, Riccardo Bonalli, Alessandro Rudi · 30 juillet 2026

  We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values. From trajectory data, we aim to estimate coefficients whose induced density f…

• Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes

  Lennon J. Shikhman, Michael Galarnyk, Aadi Dash, Nicholas A. Welsh · 30 juillet 2026

  Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark exposes simulator-truth densities for latent evaluation, while a chronological NIFTY benchmark tests only held-out market pric…

• Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration

  Dhruv Sarkar, Vaneet Aggarwal · 16 juillet 2026

  Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium. We study this regime under a contractive fast map and a non-expansive reduced slow map. We first prove a finite-horizon…

• A Provably Convergent Plug-and-Play Framework for Stochastic Bilevel Optimization

  Tianshu Chu, Dachuan Xu, Wei Yao, Chengming Yu, Jin Zhang · 14 juillet 2026

  Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named PnPBO, for developing and analyzing stochastic bilevel optimizat…

• PIVOT: Bridging Black-Scholes Implied-Volatility and Price Objectives via Differentiable J\"ackel Operator

  Raeid Saqur, Yannick Limmer, Anastasis Kratsios, Blanka Horvath, Hans Buehler · 17 juin 2026

  Modern option-learning systems operate in two coordinates: price space, where markets quote and no-arbitrage constraints are most naturally enforced, and implied volatility (IV) space, where volatility surfaces are smoothed, regularized, and evaluated. The bottleneck is interface, not approximation:…

• Bregman meets L\'evy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time

  Pierre-Louis Cauvin, Panayotis Mertikopoulos · 3 juin 2026

  We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input. To address this question in a principled manner, we begin by introducing a continuous-time…

• Error Bounds for a Diffusion Model-Based Drift Estimator

  Ioar Casado-Telletxea, Omar Rivasplata · 2 juin 2026

  Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al. (2026) introduced a novel technique for estimating the drift when the diffusion parameter is known, using discrete samples from…

• Extensions of Robbins-Siegmund Theorem with Applications in Reinforcement Learning

  Xinyu Liu, Zixuan Xie, Shangtong Zhang · 28 mai 2026

  The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is one of the most commonly used approaches for analyzing stochastic iterative algorithms in stochastic approximation and reinforcement learning (RL). However, its original form has …

• On the Communication Complexity of Decentralized Stochastic Bilevel Optimization

  Yihan Zhang, My T. Thai, Jie Wu, Hongchang Gao · 26 mai 2026

  Stochastic bilevel optimization finds widespread applications in machine learning, including meta-learning, hyperparameter optimization, and neural architecture search. To extend stochastic bilevel optimization to distributed data, several decentralized stochastic bilevel optimization algorithms hav…