Extreme Value Methods With Applications to Finance

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers—in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown distribution making as few assumptions as possible.
Extreme Value Methods with Applications to Finance concentrates on modern topics in EVT, such as processes of exceedances, compound Poisson approximation, Poisson cluster approximation, and nonparametric estimation methods. These topics have not been fully focused on in other books on extremes. In addition, the book covers:


Extremes in samples of random size
Methods of estimating extreme quantiles and tail probabilities
Self-normalized sums of random variables
Measures of market risk

Along with examples from finance and insurance to illustrate the methods, Extreme Value Methods with Applications to Finance includes over 200 exercises, making it useful as a reference book, self-study tool, or comprehensive course text.
A systematic background to a rapidly growing branch of modern Probability and Statistics: extreme value theory for stationary sequences of random variables.

Dr S.Y. Novak earned his Ph.D. at the Novosibirsk Institute of Mathematics under the supervision of Dr S.A. Utev in 1988. The Novosibirsk group forms a part of Russian tradition in Probability & Statistics that extends its roots to Kolmogorov and Markov.

Dr S.Y. Novak began his teaching carrier at the Novosibirsk Electrotechnical Institute (NETI) and Novosibirsk Institute of Geodesy, held post-doctoral positions at the University of Sussex and Eurandom (Technical University of Eindhoven), and taught at Brunel University in West London, before joining the Middlesex University (London) in 2003. He published over 40 papers, mostly on the topic of Extreme Value Theory, in which he is considered an expert.

IntroductionDistribution of ExtremesMethods of Extreme Value TheoryOrder Statistics"Blocks" and "Runs" ApproachesMethod of Recurrent InequalitiesProofsMaximum of Partial SumsErdős–Rényi Maximum of Partial SumsBasic InequalitiesLimit Theorems for MPSProofsExtremes in Samples of Random SizeMaximum of a Random Number of r.v.sNumber of ExceedancesLength of the Longest Head RunLong Match PatternsPoisson ApproximationTotal Variation DistanceMethod of a Common Probability SpaceThe Stein MethodBeyond BernoulliThe Magic FactorProofsCompound Poisson ApproximationLimit TheoryAccuracy of CP ApproximationProofsExceedances of Several LevelsCP Limit TheoryGeneral CaseAccuracy of ApproximationProofsProcesses of ExceedancesOne-level EPPEExcess ProcessComplete Convergence to CP ProcessesProofsBeyond Compound PoissonExcess ProcessComplete ConvergenceProofsStatistics of ExtremesInference on Heavy TailsHeavy-tailed distributionsEstimation MethodsTail Index EstimationEstimation of Extreme QuantilesEstimation of the Tail ProbabilityProofsValue-at-Risk. Value-at-Risk and Expected ShortfallTraditional Methods of VaR EstimationVaR and ES Estimation from Heavy-Tailed DataVaR over Different Time HorizonsTechnical Analysis of Financial DataExtremal IndexPreliminariesEstimation of the Extremal IndexProofsNormal Approximation. Accuracy of Normal ApproximationStein’s MethodSelf-Normalized Sums of r.v.s ProofsLower BoundsPreliminary ResultsFréchét–Rao–Cramér InequalityInformation IndexContinuity Moduli Tail Index and Extreme QuantilesProofsAppendixProbability DistributionsProperties of DistributionsProbabilistic Identities and InequalitiesDistancesLarge DeviationsElements of Renewal TheoryDependencePoint ProcessesSlowly Varying FunctionsUseful Identities and InequalitiesReferencesIndex