The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Christian Reichlin - One of the best experts on this subject based on the ideXlab platform.
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utility maximization with a given pricing measure when the utility is not necessarily concave
Mathematics and Financial Economics, 2013Co-Authors: Christian ReichlinAbstract:We study the problem of maximizing expected utility from terminal wealth for a non-concave utility function and for a budget set given by one fixed pricing measure. We prove the existence and several fundamental properties of a maximizer. We analyze the (non-concave) value function (indirect utility). In particular, we show that the concave envelope of the non-concave value function is the value function of the utility maximization problem for the concave envelope of the non-concave utility function. The two value functions are shown to coincide if the Underlying Probability space is atomless. This allows us to characterize the maximizers for several model classes explicitly.
Johannes Ruf - One of the best experts on this subject based on the ideXlab platform.
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PATHWISE SOLVABILITY OF STOCHASTIC INTEGRAL EQUATIONS WITH GENERALIZED DRIFT AND NON-SMOOTH DISPERSION FUNCTIONS
Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 2016Co-Authors: Ioannis Karatzas, Johannes RufAbstract:We study one-dimensional stochastic integral equations with non-smooth dispersion coefficients, and with drift components that are not restricted to be absolutely continuous with respect to Lebesgue measure. In the spirit of Lamperti, Doss and Sussmann, we relate solutions of such equations to solutions of certain ordinary integral equations, indexed by a generic element of the Underlying Probability space. This relation allows us to solve the stochastic integral equations in a pathwise sense.
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Supermartingales as Radon-Nikodym densities and related measure extensions
The Annals of Probability, 2015Co-Authors: Nicolas Perkowski, Johannes RufAbstract:Certain countably and finitely additive measures can be associated to a given nonnegative supermartingale. Under weak assumptions on the Underlying Probability space, existence and (non)uniqueness results for such measures are proven.
Adelchi Azzalini - One of the best experts on this subject based on the ideXlab platform.
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Sample selection models for discrete and other non-Gaussian response variables
Statistical Methods & Applications, 2019Co-Authors: Adelchi Azzalini, Hyoung-moon Kim, Hea-jung KimAbstract:Consider observation of a phenomenon of interest subject to selective sampling due to a censoring mechanism regulated by some other variable. In this context, an extensive literature exists linked to the so-called Heckman selection model. A great deal of this work has been developed under Gaussian assumption of the Underlying Probability distributions; considerably less work has dealt with other distributions. We examine a general construction which encompasses a variety of distributions and allows various options of the selection mechanism, focusing especially on the case of discrete response. Inferential methods based on the pertaining likelihood function are developed.
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clustering via nonparametric density estimation
Statistics and Computing, 2007Co-Authors: Adelchi Azzalini, Nicola TorelliAbstract:Although Hartigan (1975) had already put forward the idea of connecting identification of subpopulations with regions with high density of the Underlying Probability distribution, the actual development of methods for cluster analysis has largely shifted towards other directions, for computational convenience. Current computational resources allow us to reconsider this formulation and to develop clustering techniques directly in order to identify local modes of the density. Given a set of observations, a nonparametric estimate of the Underlying density function is constructed, and subsets of points with high density are formed through suitable manipulation of the associated Delaunay triangulation. The method is illustrated with some numerical examples.
Joel E Cohen - One of the best experts on this subject based on the ideXlab platform.
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every variance function including taylor s power law of fluctuation scaling can be produced by any location scale family of distributions with positive mean and variance
Theoretical Ecology, 2020Co-Authors: Joel E CohenAbstract:One of the most widely verified empirical regularities of ecology is Taylor’s power law of fluctuation scaling, or simply Taylor’s law (TL). TL says that the logarithm of the variances of a set of random variables or a set of random samples is (exactly or approximately) a linear function of logarithm of the means of the corresponding random variables or random samples: logvariance = log a + b log mean, a > 0. Ecologists have argued about the interpretation of the intercept log a and slope b of TL and about what the values of these parameters reveal about the Underlying Probability distributions of the random samples. We show here that the form and the values of the parameters of TL and of any other variance function (relationship of variance to mean in a set of samples or a family of random variables) say nothing whatsoever about the Underlying Probability distributions of the random samples (or random variables) other than that they have finite mean and variance. Specifically, given any real-valued random variable with a finite mean and a finite variance, and given any variance function (e.g., TL with specified intercept log a and slope b), we construct a family of random variables with Probability distributions of the same shape as the Probability distribution of the given random variable (i.e., that are the same up to location and scale, or in the same “location-scale family”) and that obeys the given variance function exactly (e.g., TL exactly with the given intercept log a and slope b). Every variance function can be produced by the location-scale family of any random variable with finite positive mean and finite positive variance. We illustrate some consequences of these findings by examples (e.g., for presence-absence sampling in agricultural pest control).
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Every variance function, including Taylor’s power law of fluctuation scaling, can be produced by any location-scale family of distributions with positive mean and variance
Theoretical Ecology, 2020Co-Authors: Joel E CohenAbstract:One of the most widely verified empirical regularities of ecology is Taylor’s power law of fluctuation scaling, or simply Taylor’s law (TL). TL says that the logarithm of the variances of a set of random variables or a set of random samples is (exactly or approximately) a linear function of logarithm of the means of the corresponding random variables or random samples: logvariance = log a + b log mean, a > 0. Ecologists have argued about the interpretation of the intercept log a and slope b of TL and about what the values of these parameters reveal about the Underlying Probability distributions of the random samples. We show here that the form and the values of the parameters of TL and of any other variance function (relationship of variance to mean in a set of samples or a family of random variables) say nothing whatsoever about the Underlying Probability distributions of the random samples (or random variables) other than that they have finite mean and variance. Specifically, given any real-valued random variable with a finite mean and a finite variance, and given any variance function (e.g., TL with specified intercept log a and slope b ), we construct a family of random variables with Probability distributions of the same shape as the Probability distribution of the given random variable (i.e., that are the same up to location and scale, or in the same “location-scale family”) and that obeys the given variance function exactly (e.g., TL exactly with the given intercept log a and slope b ). Every variance function can be produced by the location-scale family of any random variable with finite positive mean and finite positive variance. We illustrate some consequences of these findings by examples (e.g., for presence-absence sampling in agricultural pest control).
Nicolas Vayatis - One of the best experts on this subject based on the ideXlab platform.
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refined exponential rates in vapnik chervonenkis inequalities
Comptes Rendus De L Academie Des Sciences Serie I-mathematique, 2001Co-Authors: Robert Azencott, Nicolas VayatisAbstract:Abstract Vapnik–Chervonenkis bounds on speeds of convergence of empirical means to their expectations have been continuously improved over the years. The result obtained by M. Talagrand in 1994 [11] seems to provide the final word as far as universal bounds are concerned. However, for fixed families of Underlying Probability distributions, the exponential rate in the deviation term can be fairly improved by the more adequate Cramer transform, as shown by theorems of large deviations.
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Refined exponential rates in Vapnik–Chervonenkis inequalities
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2001Co-Authors: Robert Azencott, Nicolas VayatisAbstract:Abstract Vapnik–Chervonenkis bounds on speeds of convergence of empirical means to their expectations have been continuously improved over the years. The result obtained by M. Talagrand in 1994 [11] seems to provide the final word as far as universal bounds are concerned. However, for fixed families of Underlying Probability distributions, the exponential rate in the deviation term can be fairly improved by the more adequate Cramer transform, as shown by theorems of large deviations.
