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a-stable applications ARCH(l assume asymptotic autocorrelations behaviour Borel sets Brownian motion Chapter condition constants cn corresponding Cramer-Lundberg defined Definition denotes density df F discussion domain of attraction Embrechts Example extremal events extremal index extreme value distribution extreme value theory Figure finite finite-dimensional distributions Gaussian generalised geometric Brownian motion Gumbel Gumbel distribution Haan heavy-tailed Hence Hill estimator homogeneous Poisson process iid rvs iid sequence instance integral Laplace-Stieltjes transform large deviations Lemma limit distribution limsup linear process maxima maximum domain MDA(yl mean excess function method normalised norming constants Notes and Comments P(Mn parameter Pareto Pareto distribution periodogram point process proof properties Proposition quantile random walk regular variation regularly varying reinsurance relation sample paths Section sequence Xn SLLN stationary process stationary sequence stochastic processes subexponential Suppose tail Theorem threshold upper order statistics vector weak convergence
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Alexander J McNeil, ETH Zentrum
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Modelling Extremal Events for Insurance and Finance
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Modelling Extremal Evnts for Insurance and Finance
Modelling extremal events