arXiv research

Paper studies long-run risk optimization with dyadic impulses for unbounded processes.

Using results from our companion article [arXiv:1112.4824v2] on a Schauder approach to existence of solutions to a degenerate-parabolic partial differential equation, we solve three intertwined problems, motivated by probability theory and mathematical finance, concerning degenerate diffusion processes. We show that th…

New method estimates volatility for Lévy processes with unbounded jumps efficiently.

Study Fourier estimator for spot volatility with unbounded coefficients and jumps.

Solves open problem on universally consistent online learning with unbounded losses.

New method for Bayesian neural networks with unbounded weights.

We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertain…

New method estimates volatility for processes with jumps of unbounded variation.

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the existence of an optimal trading strategy within a class of permissible strategies -- t…

This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded framework, we extend our analysis to the more challenging unbounded case. Our methodolo…

Algorithm learns diffusion processes with high-dimensional state spaces.

LLA shows strong performance in Bayesian optimization but has unbounded search space issues.

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

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical one…

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical one…

We consider a discounted reward control problem in continuous time stochastic environment where the discount rate might be an unbounded function of the control process. We provide a set of general assumptions to ensure that there exists a smooth classical solution to the corresponding HJB equation. Moreover, some verif…

We study the convex duality method for robust utility maximization in the presence of a random endowment. When the underlying price process is a locally bounded semimartingale, we show that the fundamental duality relation holds true for a wide class of utility functions on the whole real line and unbounded random endo…

New approach to concentration inequalities for unbounded state space dynamical systems.

We describe two topologies on the space of unbounded Fredholm operators and we explain their K-theoretic relevance. In the process we also prove a very general result concerning the continuity of families of first order, elliptic boundary value problems.

The paper proves concentration inequalities for diffusion processes.

The purpose of this note is to describe, in terms of a power series, the distribution function of the exponential functional, taken at some independent exponential time, of a spectrally negative Lévy process ξwith unbounded variation. We also derive a Geman-Yor type formula for Asian options prices in a financial marke…

Two new algorithms improve performance in adversarial bandits with unbounded losses.

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e.~a least favorable frictionless market leading to the same optimal strategy and u…

Constructs unbounded Kasparov product for sphere embeddings into Euclidean space.

Unbounded convex domains have zero mean curvature on disconnected boundaries.

In most papers establishing consistency for learning algorithms it is assumed that the observations used for training are realizations of an i.i.d. process. In this paper we go far beyond this classical framework by showing that support vector machines (SVMs) essentially only require that the data-generating process sa…

The paper proves homotopy equivalences for spaces of unbounded Fredholm operators.

Golden L surface has unbounded bunching of saddle connections

The paper proves a regret bound for a sub-Gaussian mixture on unbounded data.

Enforces physical constraints in GP regression models.

This note shows how to transform high-probability to in-expectation guarantees in machine learning.

It is shown that the compactly supported identity component of the diffeomorphism group of the 2-dimensional punctured torus $\mathbb T^2_p$ is an unbounded group. It follows that the fragmentation norm of $\mathbb T^2_p$ is unbounded.

New inequalities for unbounded functions improve denoising score matching.

Study focal surfaces of wave fronts with unbounded curvatures.

Study ancient solutions on graphs with unbounded Laplacians, generalizing previous results.

Study shows unbounded Pontryagin numbers on curved manifolds.

Paper tackles online control of linear systems with unbounded noise.

This paper deals with discrete-time Markov control processes on a general state space. A long-run risk-sensitive average cost criterion is used as a performance measure. The one-step cost function is nonnegative and possibly unbounded. Using the vanishing discount factor approach, the optimality inequality and an optim…

We show that domains, that allow for convex functions with unbounded gradient at their boundary, are convex.

New algorithms optimize risk-aware selection in uncertain rewards.

New approach finds solutions to games with unbounded controls.

The paper provides gradient estimates for Neumann semigroups on manifolds with boundary under unbounded curvature conditions.

New aggregation strategy handles unbounded losses with regret bounds.

PITMonitor monitors model calibration over time with formal error guarantees.

Improved sampling from Gaussian distributions with privacy constraints.

New PAC-Bayes bounds for unbounded loss functions.

Geometric model of unbounded sl3 laminations with tropical coordinates.