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We consider the expected shortfall of accounting values, or, mathematically speaking, of random variables that are not continuous (i. e. whose cumulative distribution function is not continuous). Acerbi and Tasche show that one has to abandon the conditional expectation in order to maintain...
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Let X, Y be two discrete random variables with finite support and Xamp;#8805;Y. Suppose that the conditional distribution of Y given X can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution of X (and hence the joint distribution of...
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further study that relies on the density and cumulative probability functions of product of n random variables and the theory …
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Risk Management, Finance, Economics, Science, and many other areas. This paper develops the theory on both density and …<sub>2</sub> by using copulas to capture the structures between X<sub>1</sub> and X<sub>2</sub>. We then extend the theory by … copulas. Thereafter, we develop the theory on the median for the ratios of both Y and Z on two normal random variables X<sub>1 …
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This paper studies the approximation of extreme quantiles of random sums of heavy-tailed random variables, or more specifically, subexponential random variables. A key application of this approximation is the calculation of operational VaR (value at risk) for financial institutions, to determine...
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