The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
François Quittard-pinon - One of the best experts on this subject based on the ideXlab platform.
-
Changes of Probability Measure in finance and insurance : A synthesis
Finance, 2004Co-Authors: Olivier Le Courtois, François Quittard-pinonAbstract:This paper studies various ways of changing Probability Measures with applications to Finance and Insurance. Changes of numéraire and Esscher transforms are considered, just as pricing kernels which are, in a complementary direction, a mean of keeping a privileged Probability Measure. These approaches are compared and new insights on them are given. This article gives a unifying point of view and makes a synthesis on the subject.
Janchristian Hutter - One of the best experts on this subject based on the ideXlab platform.
-
consistency of Probability Measure quantization by means of power repulsion attraction potentials
Journal of Fourier Analysis and Applications, 2016Co-Authors: Massimo Fornasier, Janchristian HutterAbstract:This paper is concerned with the study of the consistency of a variational method for Probability Measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given Probability Measure \(\omega \) to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually \(\Gamma \)-converge to the target energy with respect to the narrow topology on the space of Probability Measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semi-definite functions from points in generic position to Probability Measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given Probability is affected by noise, we further consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of \(\Gamma \)-convergence. We show that such a discrete Measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses.
-
consistency of Probability Measure quantization by means of power repulsion attraction potentials
arXiv: Functional Analysis, 2013Co-Authors: Massimo Fornasier, Janchristian HutterAbstract:This paper is concerned with the study of the consistency of a variational method for Probability Measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given Probability Measure \omega to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually \Gamma-converge to the target energy with respect to the narrow topology on the space of Probability Measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semi-definite functions from points in generic position to Probability Measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given Probability is affected by noise, we additionally consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of \Gamma-convergence. We show that such a discrete Measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses.
Olivier Le Courtois - One of the best experts on this subject based on the ideXlab platform.
-
Changes of Probability Measure in finance and insurance : A synthesis
Finance, 2004Co-Authors: Olivier Le Courtois, François Quittard-pinonAbstract:This paper studies various ways of changing Probability Measures with applications to Finance and Insurance. Changes of numéraire and Esscher transforms are considered, just as pricing kernels which are, in a complementary direction, a mean of keeping a privileged Probability Measure. These approaches are compared and new insights on them are given. This article gives a unifying point of view and makes a synthesis on the subject.
Massimo Fornasier - One of the best experts on this subject based on the ideXlab platform.
-
consistency of Probability Measure quantization by means of power repulsion attraction potentials
Journal of Fourier Analysis and Applications, 2016Co-Authors: Massimo Fornasier, Janchristian HutterAbstract:This paper is concerned with the study of the consistency of a variational method for Probability Measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given Probability Measure \(\omega \) to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually \(\Gamma \)-converge to the target energy with respect to the narrow topology on the space of Probability Measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semi-definite functions from points in generic position to Probability Measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given Probability is affected by noise, we further consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of \(\Gamma \)-convergence. We show that such a discrete Measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses.
-
consistency of Probability Measure quantization by means of power repulsion attraction potentials
arXiv: Functional Analysis, 2013Co-Authors: Massimo Fornasier, Janchristian HutterAbstract:This paper is concerned with the study of the consistency of a variational method for Probability Measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The proof of consistency is based on the construction of a target energy functional whose unique minimizer is actually the given Probability Measure \omega to be quantized. Then we show that the discrete functionals, defining the discrete quantizers as their minimizers, actually \Gamma-converge to the target energy with respect to the narrow topology on the space of Probability Measures. A key ingredient is the reformulation of the target functional by means of a Fourier representation, which extends the characterization of conditionally positive semi-definite functions from points in generic position to Probability Measures. As a byproduct of the Fourier representation, we also obtain compactness of sublevels of the target energy in terms of uniform moment bounds, which already found applications in the asymptotic analysis of corresponding gradient flows. To model situations where the given Probability is affected by noise, we additionally consider a modified energy, with the addition of a regularizing total variation term and we investigate again its point mass approximations in terms of \Gamma-convergence. We show that such a discrete Measure representation of the total variation can be interpreted as an additional nonlinear potential, repulsive at a short range, attractive at a medium range, and at a long range not having effect, promoting a uniform distribution of the point masses.
Ross G Pinsky - One of the best experts on this subject based on the ideXlab platform.
-
spectral analysis of a family of second order elliptic operators with nonlocal boundary condition indexed by a Probability Measure
Journal of Functional Analysis, 2007Co-Authors: Iddo Benari, Ross G PinskyAbstract:Abstract Let D ⊂ R d be a bounded domain and let L = 1 2 ∇ ⋅ a ∇ + b ⋅ ∇ be a second-order elliptic operator on D . Let ν be a Probability Measure on D . Denote by L the differential operator whose domain is specified by the following nonlocal boundary condition: D L = { f ∈ C 2 ( D ¯ ) : ∫ D f d ν = f | ∂ D } , and which coincides with L on its domain. Clearly 0 is an eigenvalue for L , with the corresponding eigenfunction being constant. It is known that L possesses an infinite sequence of eigenvalues, and that with the exception of the zero eigenvalue, all eigenvalues have negative real part. Define the spectral gap of L , indexed by ν , by γ 1 ( ν ) ≡ sup { Re λ : 0 ≠ λ is an eigenvalue for L } . In this paper we investigate the eigenvalues of L in general and the spectral gap γ 1 ( ν ) in particular. The operator L and its spectral gap γ 1 ( ν ) have probabilistic significance. The operator L is the generator of a diffusion process with random jumps from the boundary, and γ 1 ( ν ) Measures the exponential rate of convergence of this process to its invariant Measure.
