Modelling Extremal Events: for Insurance and FinanceBoth in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology. |
Contents
| 1 | |
| 21 | |
Fluctuations of Sums 59 | 58 |
expx | 84 |
Fluctuations of Maxima | 113 |
1 | 169 |
Fluctuations of Upper Order Statistics | 180 |
1 | 288 |
Time Series Analysis for HeavyTailed Processes | 371 |
Special Topics | 413 |
Distribution Pax exp xa α 130 | 451 |
Appendix | 551 |
| 591 | |
| 627 | |
List of Abbreviations and Symbols | 643 |
Other editions - View all
Modelling Extremal Events: for Insurance and Finance Paul Embrechts,Claudia Klüppelberg,Thomas Mikosch No preview available - 2011 |
Common terms and phrases
a-stable absolutely continuous apply assume asymptotic autocorrelations behaviour Borel sets Brownian motion Chapter condition constants cn Cramér-Lundberg D(un defined Definition denotes density df F domain of attraction Example extremal index extreme value distribution extreme value theory Figure finite finite-dimensional distributions Gaussian generalised Gumbel Gumbel distribution Haan heavy-tailed Hence Hill estimator homogeneous Poisson process iid rvs iid sequence instance Lemma lim sup limit distribution linear process maxima maximum domain MDA(H mean excess function normalised norming constants Notes and Comments P(Mn parameter Pareto Pareto distribution periodogram point process probability process of exceedances proof Proposition quantile random walk regular variation regularly varying sample paths Section sequence Xn SLLN stable stationary process stationary sequence stochastic processes subexponential Suppose tail Theorem threshold upper order statistics variance vector weak convergence Xk,n