A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on statistical inference for nonlinear stochastic approximation with Markovian data.
problem Statistical inference for nonlinear stochastic approximation algorithms with Markovian data.
method Established a functional central limit theorem for the partial-sum process of the target parameter estimate, providing asymptotic pivotal statistics for constructing confidence intervals.
result Valid and efficient asymptotic inference method for nonlinear stochastic approximation algorithms with Markovian data.
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to …
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may be readily extended to nonlinear systems - with a reasonable expectation of suc…
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationar…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number …
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.
A novel model uses ODE-based random features to model nonlinear dynamical systems.
problem Modeling highly nonlinear dynamical systems with uncertainty quantification.
method Compositions of physics-informed random features derived from ODEs, combined with deep Gaussian processes and approximate Bayesian inference.
result The model effectively captures nonlinear behavior in real-world multivariate time series data and achieves comparable performance to other models on benchmark tasks.
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead of using two deterministic bounds, the uncertain volatility fluctuates between …
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the efficient frontier of optimal objective value versus risk of constraint violation. …
This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive system of ordinary differential equations (ODEs) for the relevant conditional distri…
Zap Q-learning is a recent class of reinforcement learning algorithms, motivated primarily as a means to accelerate convergence. Stability theory has been absent outside of two restrictive classes: the tabular setting, and optimal stopping. This paper introduces a new framework for analysis of a more general class of r…
A new algorithm solves high-dimensional nonlinear BSDEs efficiently.
problem Solving high-dimensional nonlinear backward stochastic differential equations (BSDEs).
method Transformed BSDE into a differential deep learning problem using Malliavin calculus. Discretized integrals using Euler-Maruyama method. Approximated solution with three deep neural networks. Optimized parameters using a differential learning loss function.
result Our algorithm is more accurate and faster than other methods.
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of multi-dimensional stochastic processes. Except in the simplest cases, no closed-form expressi…
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters governing the properties of this nonparametric representation. The Bayesian formalism e…
In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger c…