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.
The paper establishes conditions for strict power concavity in convolutions.
Introduces new weighted floating functions and affine surface areas.
The study proves non-existence of concave functions on specific metric spaces.
New saddle network architectures preserve convex-concave geometry in optimization problems.
The paper develops inequalities for log-concave functions and related surface areas.
Geodesic concavity and hypersymplectic structures in -structures space.
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…
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…
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…
Investigates concavity of spacetimes, showing conditions for local concavity.
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.
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…
We analyze a reweighted version of the Kikuchi approximation for estimating the log partition function of a product distribution defined over a region graph. We establish sufficient conditions for the concavity of our reweighted objective function in terms of weight assignments in the Kikuchi expansion, and show that a…
New rigidity found for 3D warped product domains.
Convexity preserved in curved surfaces moving at concave speeds.
Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of . In this article, for any closed symplectic four manifold with greater than 1, we show that there is a…
A new algorithm uses concavity in Gaussian processes to optimize decisions in bandit problems.
The paper extends risk measures to two-step approximations and studies log-concave distributions.
Study minimax risk of score estimation for log-concave distributions.
Optimizes investment under uncertain time horizons with non-concave utility.
Optimizes portfolios using CPT utility via convex optimization.
The paper analyzes portfolio selection with non-concave utility and transaction costs.
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…
New algorithm solves optimization problems without submodularity.
Strict concavity proven for growth indicator function of certain groups.
Improves SGM convergence bounds in W2-distance without strict assumptions.
Optimizes algorithms for non-concave bandit problems.
New algorithms solve complex minimax problems without needing derivatives.
A generalized optimistic method for saddle point problems with improved complexity.
Traditional dictionary learning methods are based on quadratic convex loss function and thus are sensitive to outliers. In this paper, we propose a generic framework for robust dictionary learning based on concave losses. We provide results on composition of concave functions, notably regarding super-gradient computati…
Proves existence of weighted-cscK metrics on Kähler manifolds.
A new method detects and corrects outliers using optimal transport.
Paper proposes an algorithm to solve complex minimax problems efficiently.
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the optimality of such algorithms in terms of the `total curvature'. We also show that by adj…
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
It was recently proved that embedded solutions of Euclidean hypersurface flows with speeds given by concave (convex), degree one homogeneous functions of the Weingarten map are interior (exterior) non-collapsing. These results were subsequently extended to hypersurface flows in the sphere and hyperbolic space. In the f…
In this short note we observe that the concavity of Perelman's -functional over a neighborhood of a Kähler-Ricci soliton inside the space of Kähler potentials is a direct consequence of author's solution of the variational stability problem for Kähler-Ricci solitons. Independently, we provide a rather simp…