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.
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
We extend Dupire's formula for stochastic interest rates and local volatility.
New algorithms optimize spectral risk measures, improving interpolation between average and worst-case performance.
The paper studies stochastic gradient descent with infinite variance gradients.
Unified algorithm for optimizing rewards in stochastic path problems.
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert advice, is surprisingly both worst-case optimal and adaptive to the easier stochastic …
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic continuous optimization, namely stochastic gradient descent and its variants, to such d…
Improves bandits with knapsacks guarantees for partially stochastic workloads.
Investor optimizes worst-case portfolio in uncertain markets.
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic o…
We develop two new stochastic Gauss-Newton algorithms for solving a class of non-convex stochastic compositional optimization problems frequently arising in practice. We consider both the expectation and finite-sum settings under standard assumptions, and use both classical stochastic and SARAH estimators for approxima…
New method assesses financial and cyber risks under uncertainty.
New theory explains why normalization is preferred in SGD under heavy-tailed noise.
Improved algorithms for stochastic linear bandits using tighter confidence sequences.
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
Stochastic models analyze traffic network performance.
Develops methods to simulate option prices for a specific stochastic volatility model.
Statistic dynamics of financial systems is investigated, basing on a model of randomly coupled equation system driven by stochastic Langevin force. It is found that in stable regime the noise power spectrum of the system is of 1/f^alpha form, with the exponent alpha=3/2 in case of Hermitian coupling matrices, or slight…
Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.
We introduce and analyze stochastic optimization methods where the input to each gradient update is perturbed by bounded noise. We show that this framework forms the basis of a unified approach to analyze asynchronous implementations of stochastic optimization algorithms.In this framework, asynchronous stochastic optim…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of ordering conditions on the spectral measures, which allows for analytical or numerical…
State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with t…
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
New method reveals insights about stochastic optimization methods using modified equations.
We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We proposed the stochastic ADMM to solve this complicated objective. In order to find an stationary point where the expected norm of the subgradient of corresponding augmented Lag…
Study efficient algorithms for nonconvex optimization with state-dependent Markov data.
Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Eucli…
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 …
Stochastic approximation extended to infinite dimensions, especially Banach spaces.
New approach connects stochastic gradient descent to ODE splitting schemes.
The purpose of this work is to extend the formalism of stochastic calculus to the case of spaces with local anisotropy (modeled as vector bundles with compatible nonlinear and distinguished connections and metric structures and containing as particular cases different variants of Kaluza--Klein and generalized Lagrange …
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We propose a general framework for such methods, for which we prove almost sure conve…
The study extends stochastic completeness to landmark spaces with any number of landmarks.
Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide significant improvements over stochastic gradient descent (SGD). Rigorously speak…
In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general noncon…
New methods optimize complex optimization problems with improved efficiency.
We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and achieves both faster speed and higher accuracy at every iteration than the current sta…
In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fr…
Paper develops SINNOs for approximating stochastic processes.
In the paper, we construct conservative Markov processes corresponding to the martingale solutions to the stochastic heat equation on or with values in a general Riemannian maifold, which is only assumed to be complete and stochastic complete. This work is an extension of the previous paper …
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective func…
Optimizes regret distribution in stochastic bandits for risk balance.
Paper introduces cubature method for stochastic Volterra equations.
AI models solved the Kaczmarz algorithm's worst-case complexity.
Adaptive MAB algorithms handle composite, anonymous feedback without reward interval knowledge.
Paper derives an error bound for stochastic LTI systems.
Stochastic approximation proves asymptotic normality for non-smooth problems.
New algorithm minimizes worst-case regret in uncertain, time-varying dynamics.