arXiv research

The paper addresses pricing interest rate derivatives in markets with volatility uncertainty.

We provide a general construction of time-consistent sublinear expectations on the space of continuous paths. It yields the existence of the conditional G-expectation of a Borel-measurable (rather than quasi-continuous) random variable, a generalization of the random G-expectation, and an optional sampling theorem that…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space), equivalently, on random closed sets. …

New model for Knightian uncertainty with jumps.

For $α\in (1,2)$, we present a generalized central limit theorem for $α$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, p…

Paper generalizes extragradient methods for solving equations and inclusions with improved convergence rates.

We study the existence of optimal actions in a zero-sum game $\inf_τ\sup_PE^P[X_τ]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_τ\mathcal{E}(X_τ)$ for a class of sublinear expectations $\mathcal{E}(\cdot)$ such as the $G$-expectation. We show that …

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control …

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strate…

The paper generalizes Feynman-Kac formula for volatility uncertainty.

Posterior sampling-based EI achieves sublinear regret bounds for expensive function optimization.

Paper studies portfolio investment under volatility uncertainty and short-sale constraints, improving risk-adjusted returns.

Average signature of 2-bridge knots approximates sqrt(2c/π).

This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $σ$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff…

For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a $G$-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…

We study the problem of estimating the expected reward of the optimal policy in the stochastic disjoint linear bandit setting. We prove that for certain settings it is possible to obtain an accurate estimate of the optimal policy value even with a number of samples that is sublinear in the number that would be required…

New algorithms reduce private bandit regret to nearly non-private levels.

Greedy algorithm achieves sublinear regret for various distributions.

New framework guides resource usage to achieve sublinear regret in adversarial settings.

New algorithm tackles delayed feedback in Lipschitz bandits with sublinear regret.

New RL algorithm achieves sublinear regret and constraint violation without simulators.

A corrected EI acquisition function handles noisy observations in Bayesian optimization.

Develops a new option pricing model under G-expectation framework.

The paper shows how sublinear biLipschitz equivalences affect Morse boundaries of metric spaces.

Gradient EM converges globally for over-parameterized Gaussian mixtures.

Paper establishes no-regret property for practical EGO optimization.

Paper predicts high-frequency futures return directions using mean-uncertainty methods.

Novel numerical scheme for G-heat equation with uncertainty.

Algorithm maximizes revenue-risk by estimating price impact kernel and optimizing control problems.

New methods optimize functions faster with less gradient accuracy needed.

We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and utilizes the expected improvement idea from Bayesian global optimization. We adapt…

Paper recovers uncertainty from dynamic valuation rules.

Sharp stability threshold found for deep residual architectures.

Study local exploration on dynamic graphs with time-varying edges.

GP-PSRL achieves sublinear regret for continuous control with unbounded state space.

We propose a randomized nonmonotone block proximal gradient (RNBPG) method for minimizing the sum of a smooth (possibly nonconvex) function and a block-separable (possibly nonconvex nonsmooth) function. At each iteration, this method randomly picks a block according to any prescribed probability distribution and solves…

Abundant literature has been published on approximation methods for the forward initial margin. The most popular ones being the family of regression methods. This paper describes the mathematical foundations on which these regression approximation methods lie. We introduce mathematical rigor to show that in essence, al…

Sublinear LSVI via LSH reduces runtime to sublinear in actions.

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded proper metric space. For example, the sublinear Higson corona of n-dimensional E…

Optimal wealth strategy derived for jump-diffusion models with liabilities.

We consider stochastic gradient descent and its averaging variant for binary classification problems in a reproducing kernel Hilbert space. In the traditional analysis using a consistency property of loss functions, it is known that the expected classification error converges more slowly than the expected risk even whe…

We consider a multiobjective multiarmed bandit problem with lexicographically ordered objectives. In this problem, the goal of the learner is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multidimensional for…

New variance-reduction methods solve stochastic composite inclusions.

We give a proof of the sublinear tracking property for sample paths of random walks on various groups acting on spaces with hyperbolic-like properties. As an application, we prove sublinear tracking in Teichmueller distance for random walks on mapping class groups, and on Cayley graphs of a large class of finitely gene…

We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.

We study the non-stationary stochastic multiarmed bandit (MAB) problem and propose two generic algorithms, namely, the limited memory deterministic sequencing of exploration and exploitation (LM-DSEE) and the Sliding-Window Upper Confidence Bound# (SW-UCB#). We rigorously analyze these algorithms in abruptly-changing a…

This work creates a CS for non-negative heavy-tailed data with bounded mean.

Study geodesics on graphs with random lengths, proving bi-infinite paths exist.