Reader Guideline

1. Risk Theory

The Ruin Problem

The Cramer-Lundberg Estimate

Ruin Theory for Heavy-Tailed Distributions

The Cramer-Lundberg for Large Claims

2. Fluctuations of Sums

The Laws of Large Numbers

The Central Limit Problem

Refinements of the CLT

The Functional CLT: Brownian Motion Appears

Random Sums

3. Fluctuations of Maxima

Limit Problems for Maxima

Weak Convergence of Maxima Under Affine Transformations

Maximum Domains of Attraction and and Norming Constants

Generalized Extreme Value Distribution and Generalized Pareto Distribution

Almost Sure Behavior of Maxima

4. Fluctuations of Upper Order Statistics

Order Statistics

The Limit Distribution of Upper Order Statistics

The Limit Distribution of Randomly Indexed Upper Order Statistics

Some Extreme Value Theory for Stationary Sequences

5. An Approach to Extremes via Point Processes

Basic Facts About Point Processes

Weak Convergence of Point Processes

Point Processes of Exceedances

Applications of Point Process Methods to IID Sequences

Some Extreme Value Theory for Linear Processes

6. Statistical Methods for Extremal Events

Exploratory Data Analysis for Extremes

Parameter Estimation for the Generalized Extreme Value Distribution

Estimating Under Maximum Domain of Attraction Conditions

Fitting Excesses Over a Threshold

7. Time Series Analysis for Heavy-Tailed Processes

A Short Introduction to Classical Time Series Analysis

Heavy-Tailed Time Series

Estimation of the Autocorrelation Function

Estimation of the Power Transfer Function

Parameter Estimation for ARMA Processes

Some Remarks about Heavy0Tailed Nonlinear Models

8. Special Topics

The Extremal Index

A Large Claim Index

When and How Ruin Occurs

Perpetuities and ARCH Processes

On the Longest Success Run

Some Results on Large Deviations

Reinsurance Treaties

Stable Processes

Self Similarity