arXiv research

The paper analyzes portfolio selection with non-concave utility and transaction costs.

A new method detects and corrects outliers using optimal transport.

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…

In this paper we extend the setting of the online prediction with expert advice to function-valued forecasts. At each step of the online game several experts predict a function, and the learner has to efficiently aggregate these functional forecasts into a single forecast. We adapt basic mixable (and exponentially conc…

The market impact (MI) of Volume Weighted Average Price (VWAP) orders is a convex function of a trading rate, but most empirical estimates of transaction cost are concave functions. How is this possible? We show that isochronic (constant trading time) MI is slightly convex, and isochoric (constant trading volume) MI is…

Investigates portfolio selection with transaction costs and stochastic volatility, using deep learning for computation.

Investigates how rebalancing frequency and transaction costs affect log-optimal portfolios.

Paper examines costs of using wrong price impact models in trading.

Enhances LMC for log-concave sampling, reducing computational cost.

Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.

Pushing a little forward an approach proposed by Villani, we are going to prove that in the Riemannian setting the condition $\nabla^2 f< g$ implies that $f$ is $c$-concave with respect to the quadratic cost as soon as it has a sufficiently small $C^1$-norm. From this, we deduce a sufficient condition for the optimalit…

Paper proposes efficient cost functions for automated market makers in DeFi.

We study the problem of super-replication for game options under proportional transaction costs. We consider a multidimensional continuous time model, in which the discounted stock price process satisfies the conditional full support property. We show that the super-replication price is the cheapest cost of a trivial s…

A new sampling method for log-concave distributions with warm starts and barriers.

The paper establishes conditions for strict power concavity in convolutions.

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…

We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for co…

This work overcomes bias in concave multi-objective reinforcement learning.

This paper optimizes Bayesian estimation for log-concave models using Langevin Monte-Carlo.

Introduces new weighted floating functions and affine surface areas.

A new sampling method reduces computational cost for high-dimensional log-concave distributions.

The study proves non-existence of concave functions on specific metric spaces.

A new algorithm reduces online exp-concave optimization runtime.

New saddle network architectures preserve convex-concave geometry in optimization problems.

New stability bounds for Sinkhorn's algorithm in entropic optimal transport.

The paper develops inequalities for log-concave functions and related surface areas.

The paper provides tight bounds for improving multi-armed bandits problem.

Geodesic concavity and hypersymplectic structures in $G2$-structures space.

Develops a new method for optimizing portfolios in stochastic markets.

Unified routing and arbitrage with concave continuation.

Log-concavity proven for multinomial likelihoods under specific constraints.

Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gr…

Paper finds convexity in translating solitons for concave flows.

We explain a general construction through which concave elliptic operators on complex manifolds give rise to concave functions on cohomology. In particular, this leads to generalized versions of the Khovanskii-Teissier inequalities.

A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximat…

Study timelike Ricci curvature bounds via optimal transport with Orlicz-type costs.

Estimates log-concave densities in graphical models using tent functions.

We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these concavity properties directly for a large class of flows by applying a concavity maximum principle argument to the corresponding level set f…

In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the lev…

Investigates concavity of spacetimes, showing conditions for local concavity.

Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.

Decision maker's preferences are often captured by some choice functions which are used to rank prospects. In this paper, we consider ambiguity in choice functions over a multi-attribute prospect space. Our main result is a robust preference model where the optimal decision is based on the worst-case choice function fr…

We construct a compact symplectic manifold with a Hamiltonian circle action for which the Duistermaat-Heckman function is not log-concave.

ICCNLS models complex relationships as convex and concave components.

A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures.

RO-TD learns sparse value functions efficiently.

We analyze the classical model of compound interest with a constant per-period payment and interest rate. We examine the outstanding balance function as well as the periodic payment function and show that the outstanding balance function is not generally concave in the interest rate, but instead may be initially convex…

The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…