Related papers: Log-concave functions and transformations thereof
In this note, we show that the convolution of a discrete symmetric log-concave distribution and a discrete symmetric bimodal distribution can have any strictly positive number of modes. A similar result is proved for smooth distributions.
The motivation behind this paper is threefold. Firstly, to study, characterize and realize operator concavity along with its applications to operator monotonicity of free functions on operator domains that are not assumed to be matrix…
Optimization of conditional convex risk measure is a central theme in dynamic portfolio selection theory, which has not yet systematically studied in the previous literature perhaps since conditional convex risk measures are neither random…
Anari, Gharan, and Vinzant proved (complete) log-concavity of the basis generating functions for all matroids. From the viewpoint of combinatorial Hodge theory, it is natural to ask whether these functions are "strictly" log-concave for…
We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the…
This paper considers the difference of stop-loss payoffs where the underlying is a difference of two random variables. The goal is to study whether the comonotonic and countermonotonic modifications of those two random variables can be used…
We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type $\mathrm{Tr}\,f(\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2})$ and symmetric (anti-) norm functions of the form…
In an incomplete Brownian-motion market setting, we propose a convex monotonic pricing functional for nonattainable bounded contingent claims which is compatible with prices for attainable claims. The pricing functional is defined as the…
We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these…
We show a surprising connexion between a property of the inf convolution of a family of convex lower semicontinuous functions and the fact that the intersection of maximal cyclically monotone graphs is the critical set of a bipotential. We…
Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable…
Sampling from Gibbs distributions and computing their log-partition function are fundamental tasks in statistics, machine learning, and statistical physics. While efficient algorithms are known for log-concave densities, the worst-case…
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
We present a theory of expected utility with state-dependent linear utility functions for monetary returns, that incorporates the possibility of loss-aversion. Our results relate to first order stochastic dominance, mean-preserving spread,…
Using calculus we show how to prove some combinatorial inequalities of the type log-concavity or log-convexity. It is shown by this method that binomial coefficients and Stirling numbers of the first and second kinds are log-concave, and…
In this paper, we study when we might expect the optimization curve induced by gradient descent to be \emph{convex} -- precluding, for example, an initial plateau followed by a sharp decrease, making it difficult to decide when optimization…
By making use of the familiar Mathieu series and its generalizations, the authors derive a number of new integral representations and present a systematic study of probability density functions and probability distributions associated with…
We propose a notion of operator monotonicity for functions of several variables, which extends the well known notion of operator monotonicity for functions of only one variable. The notion is chosen such that a fundamental relationship…
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…