Results 11 to 20 of about 87 (65)

Robust risk aggregation with neural networks. [PDF]

Math Financ, 2020
Abstract We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a current best guess for the distribution, called reference measure, is available.
Eckstein S, Kupper M, Pohl M.
europepmc   +2 more sources

Nearly comonotone approximation [PDF]

Proceedings of the American Mathematical Society, 1975
This paper obtains estimates on the degree of nearly comonotone approximation which extend and improve the estimate obtained by Newman, Passow, and Raymon. In particular, the restriction that f
openaire   +2 more sources

A counterexample in comonotone approximation in $L^p$ space [PDF]

Colloquium Mathematicum, 1993
For \(f\in C^k[-1,1]\), \(k\in\mathbb{N}\) fixed, let \(e_n^{(k)} (f)_p\) denote the best approximation to \(f\) in the \(L_p\)-metric by algebraic polynomials \(p_n\) of degree at most \(n\) which are comonotone with \(f\), i.e. by polynomials \(p_n\) with the property \(p_n^{(k)} (x)f^{(k)} (x)\geq 0\) for \(x\in [-1,1]\).
Wu, Xiang, Zhou, Song Ping
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Positive results and counterexamples in comonotone approximation II

Journal of Approximation Theory, 2012
Let \(\mathbb{P}_{n}\) be the linear space of polynomials of degree at most \(n-1\). For a continuous function \(f\) in an interval \([a,b]\), the degree of best approximation is denoted by \[ E_{n}(f, [a,b]) = \inf \{ \|f-P_{n}\|_{[a,b]}, P_{n}\in \mathbb{P}_{n}\}. \] For \(s\geq1\), let \(\mathbf{Y}_{s} ([a,b])\) denote the family of all subsets \(Y_{
Dany Leviatan, Igor A. Shevchuk, O. V. Vlasiuk   +2 more
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Shape Preserving Interpolation Using Rational Cubic Ball Function and Its Application in Image Interpolation

Mathematical Problems in Engineering, Volume 2017, Issue 1, 2017., 2017
New rational cubic Ball interpolation with one parameter is proposed for shape preserving interpolation such as positivity, monotonicity, and convexity preservations and constrained data lie on the same side of the given straight line. To produce shape preserving interpolant, the data dependent sufficient condition is derived on the parameter.
Samsul Ariffin Abdul Karim, Azizan Saaban, Suzanne M. Shontz   +2 more
wiley   +1 more source

Sum of Bernoulli Mixtures: Beyond Conditional Independence

Journal of Probability and Statistics, Volume 2014, Issue 1, 2014., 2014
We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the ...
Taehan Bae, Ian Iscoe, Aera Thavaneswaran   +2 more
wiley   +1 more source

Comonotonic Approximations for the Sum of Log Unified Skew Normal Random Variables: Application in Finance and Actuarial Science [PDF]

Journal of Data Science, 2021
The classical works in finance and insurance for modeling asset returns is the Gaussian model. However, when modeling complex random phenomena, more flexible distributions are needed which are beyond the normal distribution. This is because most of the financial and economic data are skewed and have ＂fat tails＂.
Arjun K. Gupta, Mohammad A. Azizb
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Multivariate Fréchet copulas and conditional value‐at‐risk

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 7, Page 345-364, 2004., 2004
Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas.
Werner Hürlimann
wiley   +1 more source

Equivalence between various Shape Preserving Approximations of periodic functions

Researches in Mathematics
We show that the validity of Jackson-type estimates in comonotone and coconvex approximations of continuous $2\pi$-periodic functions by trigonometric polynomials is equivalent to the validity of the corresponding estimates of approximation by continuous
D. Leviatan, O.V. Motorna, I.O. Shevchuk
doaj   +1 more source

Efficiency in Pure‐Exchange Economies With Risk‐Averse Monetary Utilities

Mathematical Finance, Volume 36, Issue 1, Page 99-117, January 2026.
ABSTRACT We study Pareto efficiency in a pure‐exchange economy where agents' preferences are represented by risk‐averse monetary utilities. These coincide with law‐invariant monetary utilities, and they can be shown to correspond to the class of monotone, (quasi‐)concave, Schur concave, and translation‐invariant utility functionals. This covers a large
Mario Ghossoub, Michael B. Zhu
wiley   +1 more source