arXiv research

Optimal control in changing systems without strong convexity assumptions.

This paper tackles cost-sensitive portfolio optimization under ambiguous return distributions.

Efficient algorithm for unknown linear systems with convex costs.

We study online optimization in a setting where an online learner seeks to optimize a per-round hitting cost, which may be non-convex, while incurring a movement cost when changing actions between rounds. We ask: \textit{under what general conditions is it possible for an online learner to leverage predictions of futur…

This study optimizes trading and arbitrage in decentralized finance's CPMs, revealing convexity costs and developing efficient strategies.

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite number of transfers are possible. The paper presents an approach to measure risks…

Study uses weak transport for non-convex costs in fixed-income markets.

New method calculates super-hedging prices with transaction costs.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strong…

Optimal crypto asset routing with CFMMs, including fixed costs.

OMGD algorithm optimizes online convex optimization with switching costs and delayed gradients.

Designs a neural network to reduce training cost by mapping to higher dimensions.

We identify a condition for regularity of optimal transport maps that requires only three derivatives of the cost function, for measures given by densities that are only bounded above and below. This new condition is equivalent to the weak Ma-Trudinger-Wang condition when the cost is $C^4$. Moreover, we only require (n…

We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no arbitrage condition im…

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost function over a continuous space. We propose a stochastic mirror descent algorithm and …

SCaLE tackles dynamic regret in noisy bandit feedback with switching costs.

Convex duality for two two different super--replication problems in a continuous time financial market with proportional transaction cost is proved. In this market, static hedging in a finite number of options, in addition to usual dynamic hedging with the underlying stock, are allowed. The first one the problems consi…

Study on regularity of optimal transport maps on convex domains with quadratic cost.

New algorithm controls linear systems with bandit feedback, achieving optimal regret.

Deep Hedging learns risk-neutral vol dynamics for option pricing.

Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process are proved to be equivalent to the curvature condition $\Ric-\nn Z\ge - K$ and t…

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…

The paper improves competitive and dynamic regret bounds for smoothed online learning.

We consider an investor with constant absolute risk aversion who trades a risky asset with general Ito dynamics, in the presence of small proportional transaction costs. Kallsen and Muhle-Karbe (2012) formally derived the leading-order optimal trading policy and the associated welfare impact of transaction costs. In th…

Paper tackles online control of linear systems with unbounded noise.

New algorithms improve on consistency and robustness in convex function chasing with black-box advice.

A new method for optimal transport using neural ODEs that preserves marginal constraints.

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

In the field of optimal transport theory, an optimal map is known to be a gradient map of a potential function satisfying cost-convexity. In this paper, the Jacobian determinant of a gradient map is shown to be log-concave with respect to a convex combination of the potential functions when the underlying manifold is t…

This paper presents a stochastic model for discrete-time trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets. The model does not assume the existence of a cash account/numeraire. In addition to classical frictionless markets and markets with …

We study Smoothed Online Convex Optimization, a version of online convex optimization where the learner incurs a penalty for changing her actions between rounds. Given a $Ω(\sqrt{d})$ lower bound on the competitive ratio of any online algorithm, where $d$ is the dimension of the action space, we ask under what conditio…

New curvature measure for optimal transport with specific cost function.

Develops risk measures for markets with constraints and costs.

Study weak super Ricci flow through neckpinch in metric measure spaces.

This paper accelerates distributed convex optimization by mitigating ill-conditioning issues.

Explicit robust hedging strategies for convex or concave payoffs under a continuous semimartingale model with uncertainty and small transaction costs are constructed. In an asymptotic sense, the upper and lower bounds of the cumulative volatility enable us to super-hedge convex and concave payoffs respectively. The ide…

New research extends optimal transport map breakdown properties to general costs.

Paper improves COCO problem, reducing constraint violation at the cost of slightly more regret.

Optimal benchmark design varies based on costs in financial manipulation.

Optimizes portfolios with discrete units using simulated annealing.

Parallel computing has played an important role in speeding up convex optimization methods for big data analytics and large-scale machine learning (ML). However, the scalability of these optimization methods is inhibited by the cost of communicating and synchronizing processors in a parallel setting. Iterative ML metho…

In this note, we study the utility maximization problem on the terminal wealth under proportional transaction costs and bounded random endowment. In particular, we restrict ourselves to the numéraire-based model and work with utility functions only supporting R+. Under the assumption of existence of consistent price sy…

Let $X$ and $Y$ be domains of $\mathbb{R}^n$ equipped with respective probability measures $μ$ and $ν$. We consider the problem of optimal transport from $μ$ to $ν$ with respect to a cost function $c: X \times Y \to \mathbb{R}$. To ensure that the solution to this problem is smooth, it is necessary to make several ass…

Optimal DP mechanisms for vector queries are found to be staircase distributions.

We consider fractional Black-Scholes market with proportional transaction costs. When transaction costs are present, one trades periodically i.e. we have the discrete trading with equidistance $n^{-1}$ between trading times. We derive a non trivial hedging error for a class of European options with convex payoff in the…

We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive rat…

In this paper, the online variants of the classical Frank-Wolfe algorithm are considered. We consider minimizing the regret with a stochastic cost. The online algorithms only require simple iterative updates and a non-adaptive step size rule, in contrast to the hybrid schemes commonly considered in the literature. Seve…

New method improves MAP inference for CGMs on path graphs, avoiding approximation and maintaining integrality.