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Extreme market risk and extreme value theory
Mathematics and Computers in Simulation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abhay K. Singh +2 more
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Extreme Returns From Extreme Value Stocks
The Journal of Investing, 2005Investigations into value-based ‘anomalies’ such as the P/E effect typically sort shares into quintiles, or at most deciles. These are blunt instruments. We test whether most of the extra value in the lower end of the P/E spectrum is to be found in the very lowest P/E shares, and whether the worst investments reside in the few shares with the highest P/
Anderson, K., Brooks, Chris
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Extreme value analysis in biometrics
Biometrical Journal, 2009AbstractWe review some approaches of extreme value analysis in the context of biometrical applications. The classical extreme value analysis is based on iid random variables. Two different general methods are applied, which will be discussed together with biometrical examples.
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How to probe for an extreme value
ACM Transactions on Algorithms, 2010In several systems applications, parameters such as load are known only with some associated uncertainty, which is specified, or modeled, as a distribution over values. The performance of the system optimization and monitoring schemes can be improved by spending resources such as time or bandwidth in observing or
Ashish Goel +2 more
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Value at Risk and Extreme Values
IFAC Proceedings Volumes, 1998Abstract this paper gives a general exposition of the subject of Value at Risk (VaR), which is now considered as a standard measure of market risks. It is defined as the maximal loss of the portfolio for a given probability over a given period. This measure is sensitive to the tails of the distribution of returns; extreme value theory is used here to
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Testing Extreme Value Conditions
Extremes, 2002A modification of the Cramér-von Mises statistics for testing the tail behaviour of i.i.d. sample CDF \(F\) is considered. Its version for nonnegative tail index \(\gamma\) is of the form \[ T_{k,n}=\int \left( {1\over \hat\gamma} (\log X_{n-[kt],n}-\log X_{n-k,n})+\log t \right)^2 t^2\, dt, \] where \(X_{i,n}\) is the \(i\)th order statistics, \(\hat ...
Dietrich, D +2 more
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The Laplacian and Mean and Extreme Values
The American Mathematical Monthly, 2016The Laplace operator is pervasive in many important mathematical models, and fundamental results such as the Mean Value Theorem for harmonic functions, and the Max- imum Principle for super-harmonic functions are well-known. Less well-known is how the Laplacian and its powers appear naturally in a series expansion of the mean value of a func- tion on a
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Approximations for Bivariate Extreme Values
Extremes, 2000Let \((X,Y)\) denote a random vector with distribution function (d.f.) \(F\) and suppose that both \(X\) and \(Y\) are standardized to have \[ \text{Pr}(X\leq x)=\text{Pr}(Y\leq x)=\exp(-x^{-1}),\quad x>0. \] In recent years a number of statistical models have been proposed for extreme values of \((X,Y).\) The basis for these models is the assumption ...
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Value-at-risk and extreme returns [PDF]
Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. The largest risks are modelled parametrically, while smaller risks are captured by the non-parametric empirical distribution function.
Jón Daníelsson, Casper G. de Vries
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On selecting an extreme value distribution
Zeitschrift für Operations Research, 1988In a recent paper Hernandez and Johnson (1984) have given a procedure based on Bayesian statistical inference for selecting an extreme-value distribution to “best” fit available data. In this note we give an alternative derivation of part of their results.
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