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Bounds for Functions of Dependent Risks 总被引:1,自引:0,他引:1
The problem of finding the best-possible lower bound on the distribution of a non-decreasing function of n dependent risks is solved when n=2 and a lower bound on the copula of the portfolio is provided. The problem gets much more complicated in arbitrary dimensions. When no information on the structure of dependence of the random vector is available, we provide a bound on the distribution function of the sum of risks which we prove to be better than the one generally used in the literature. 相似文献
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Paul Embrechts 《Quantitative Finance》2013,13(6):402-404
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Due to the current credit crisis, critical questions are beingasked concerning some of the quantitative methods used in riskmanagement under the Basel II proposals. In this paper I havegiven a critical look at Extreme Value Theory and Copulas. Boththeir potential applications and the possible caveats are discussed,and this mainly with the subprime crisis as a background. 相似文献
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We describe a numerical procedure to obtain bounds on the distribution function of a sum of n dependent risks having fixed marginals. With respect to the existing literature, our method provides improved bounds and
can be applied also to large non-homogeneous portfolios of risks. As an application, we compute the VaR-based minimum capital
requirement for a portfolio of operational risk losses.
JEL Classification G20 · 60E15 · 91B30 相似文献
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Paul Embrechts Ph.D. Sidney I. Resnick Ph.D. Gennady Samorodnitsky Ph.D. 《North American actuarial journal : NAAJ》2013,17(2):30-41
The financial industry, including banking and insurance, is undergoing major changes. The (re)insurance industry is increasingly exposed to catastrophic losses for which the requested cover is only just available. An increasing complexity of financial instruments calls for sophisticated risk management tools. The securitization of risk and alternative risk transfer highlight the convergence of finance and insurance at the product level. Extreme value theory plays an important methodological role within risk management for insurance, reinsurance, and finance. 相似文献
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Copulas: A Personal View 总被引:1,自引:0,他引:1
Paul Embrechts 《The Journal of risk and insurance》2009,76(3):639-650
Copula modeling has taken the world of finance and insurance, and well beyond, by storm. Why is this? In this article, I review the early start of this development, discuss some important current research, mainly from an applications point of view, and comment on potential future developments. An alternative title of the article would be “Demystifying the copula craze.” The article also contains what I would like to call the copula must‐reads . 相似文献
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Transform methods, together with the fast Fourier transform algorithm, can be used to compute various quantities of interest in risk theory and insurance mathematics. These include the total claim size distribution at a fixed time, the mean and variance of the claim size process as a function of time in the Sparre-Andersen model, and the probability of ruin. The associated discretization error can be reduced by applying Richardson's deferred approach to the limit. A theorem is given that puts the use of this technique on a mathematical basis in the context of compound distributions. 相似文献