Statistical Methods

The goal of this course is to provide concepts and techniques from probability theory and statistics that are widely used in the actuarial and financial industry.

The topics covered are Markov chains, survival analysis, time series analysis, nonparametric statistics, stochastic dependence, and extreme value theory.

• Markov chains provide a basic framework to model the dynamic (discrete-time) behavior of objects/individuals over time. Examples of applications are modeling the dynamics of credit ratings of a corporate bond portfolio and the modeling of a disability insurance portfolio.

• Survival analysis considers the modeling of durations. Examples of durations relevant for the financial and actuarial industry are:  the time-to-death for life insurance policies, the time-to-prepayment of a loan or the time-to-early termination of a contract.

• The topic time series analysis discusses vector autoregressive (VAR) models, GARCH processes, and provides an introduction to the pitfalls and tools to deal with non-stationary time series. Time series models are used, for example, in economic scenario generators and asset management.

• Nonparametric statistics considers statistical inference, mainly estimation, in case it is not assumed that the underlying probability distribution follows a parametric model. Estimation of the distribution function and the density is studied in some detail, whereas nonparametric regression is briefly considered.

• Stochastic dependence of risks is crucial in insurance, e.g., dependence between losses, dependence between frequency and severity, or dependence of the different risks a financial institution faces. Stochastic dependence is considered in general, but the emphasis is on copulas.

• Extreme value theory is indispensable when dealing with catastrophes, like those caused by natural hazards. We consider the univariate theory and the corresponding actuarial applications in some detail. In the multivariate case we focus on tail dependence.

Learning outcomes

Having completed this course the participant should have:

• Understand and apply the techniques

• Understand and review (empirical) applications of the techniques/models

• Gourieroux, C. and J. Jasiak, The econometrics of individual risk: credit, insurance, and marketing, Princeton University Press, 200. (Chapter 6, 7 and 8)

• McNeil, A.J., R. Frey, and P. Embrechts, Quantitative risk management: concepts, techniques, and tools, Princeton University Press, 2005. (Chapters 3.3, 4, 5, and 7)

• Verbeek, M., A guide to modern econometrics, Wiley, 3rd edition 2008. (Chapters 8 and 9)

• Slides

Software

• EViews

• R and R Studio

#### Prerequisites

Introductory courses in analysis, linear algebra, probability theory, mathematical statistics, and a course covering ARMA models (for time series).

Exam

Written exam

Teachers
Prof. dr. J. (John)  Einmahl

Dr. R. (Ramon) van den Akker