Risk Models (1 º Sem 2020/2021)

• Klugman, S.A., Panjer, H.H. and Willmot, G.E. (2012), Loss Models - From data to decisions, 4th  Edition, John Wiley & Sons, Inc., New-Jersey.

• Hesterberg, T., Monaghan, S., Moore, D.S., Clipson, A., Epstein, R. (2003), Bootstrap Methods and Permutation Tests (http://bcs.whfreeman.com/pbs/cat_160/PBS18.pdf), companion chapter 18 to The practice of Business Statistics by David S. Moore, MCCabe, Duckworth and Sclove.

• Casella, G. and Berger, R. (2002), Statistical Inference (Second Edition). Duxbury Press.

• Efron, B. and Tibshirami, R.J. (1993), An Introduction to the Bootstrap, Chapman & Hall, New-York.

• Ross, S.M. (2002) Simulation, 3rd Edition, Academic Press.

• Seila, A., Ceric,V. and Tadikamalla,P. (2003), Applied Simulation Modeling, Duxbury Applied Series.

• Sharma, S. (1996) Applied Multivariate Techniques,John Wiley & Sons Inc., New-York.

• Wasserman, L. (2004), All of Statistics: A Concise Course in Statistical Inference, New York, Springer.

1. Review of basic statistical concepts   

1.1.    Introduction - Population versus sample   

1.2.    Summarizing information            

1.2.1. Location, variability and other characteristics of a data collection            

1.2.2. Measures of relationship between variables            

1.2.3. Basics of Principal Components Analysis (PCA)   

1.3.    Sampling and sampling distribution   

1.4.    Point estimation with emphasis on measures of quality   

1.5.    Interval estimation   

1.6.    Tests of hypothesis

2. Non-parametric estimation  

2.1.   The empirical distribution for complete individual data 

2.2.   The empirical distribution for grouped data 

2.3.   Kernel density models

3. Frequentist estimation   

3.1.   Methods of moments and percentile matching   

3.2.   Maximum likelihood estimation (individual, grouped, censored and truncated data)   

3.3.   Variance and interval estimation   

3.4.   Non-normal confidence intervals

4. Bayesian estimation    

4.1. Introduction    

4.2. Definitions and Bayes' theorem    

4.3. Inference and prediction    

4.4. Conjugate prior distributions 

5. Model selection 

5.1. Introduction 

5.2. Representation of the data and model 

5.3. Graphical comparison of the density and distribution functions 

5.4. Hypothesis tests 

5.5. Selecting a model

6. Simulation

6.1. Basics of simulation

6.2. Examples of simulation in actuarial modeling and finance

7. An introduction to the bootstrap 

7.1. Introduction to bootstrapping 

7.2. Bootstrap distributions and standards errors 

7.3. Bootstrap confidence intervals 

7.4. Significance testing using permutation tests