Syllabus: M349P

ACTUARIAL STATISTICAL ESTIMATES

Textbook: Klugman, S.A., Panjer, H.H. and Willmot, G.E., Loss Models: From Data to Decisions, Fourth Edition, 2012

Responsible party: Alisa Havens Walch and Mark Maxwell, August 2014

Prerequisite

Mathematics M339J and either M340L or M341 with a grade of at least C-. 

Please note that thorough knowledge of calculus, probability, and statistics will be assumed.

Description of the Course: M 349P Probability Models with Actuarial Applications covers statistical estimation procedures for random variables and related quantities in actuarial models.

This is an actuarial capstone course and students are expected to do some independent learning and improve verbal and written acumen.  Three graded components of the course are 1) communication, 2) content mastery, and 3) contribution to class.  This class carries the Independent Inquiry Flag.  This class carries the Quantitative Reasoning flag.  

Meets with M389P, the corresponding graduate-course number.  Offered every spring semester only.  This is a 3-credit course.

 

[Chapters 13 – 16 have a combined weight of 20% - 25% of the SOA Exam C]

PART IV PARAMETRIC STATISTICAL METHODS  

13 Frequentist estimation 

       13.1 Method of moments and percentile matching 

       13.2 Maximum likelihood estimation 

       13.3 Variance and interval estimation 

       13.4 Non-normal confidence intervals 

       13.5 Maximum likelihood estimation of decrement probabilities 

14 Frequentist Estimation for discrete distributions

       14.1 Poisson 

       14.2 Negative binomial 

       14.3 Binomial 

       14.4 The (a, b, 1) class 

       14.5 Compound models  [Not Covered]

       14.6 Effect of exposure on maximum likelihood estimation 

15 Bayesian estimation 

       15.1 Definitions and Bayes’ theorem 

       15.2 Inference and prediction 

       15.3 Conjugate prior distributions and the linear exponential family 

       15.4 Computational issues 

16 Model selection 

       16.1 Introduction 

       16.2 Representations of the data and model 

16.3 Graphical comparison of the density and distribution functions 

       16.4 Hypothesis tests 

       16.5 Selecting a model 

 

[Chapters 17 – 19 have a combined weight of 20% - 25% of the SOA Exam C]

PART V CREDIBILITY 

17 Introduction and Limited Fluctuation Credibility 

       17.1 Introduction 

       17.2 Limited fluctuation credibility theory 

       17.3 Full credibility 

       17.4 Partial credibility 

       17.5 Problems with the approach 

       17.6 Notes and References 

18 Greatest accuracy credibility

       18.1 Introduction 

       18.2 Conditional distributions and expectation 

       18.3 The Bayesian methodology 

       18.4 The credibility premium 

       18.5 The Buhlmann model 

       18.6 The Buhlmann-Straub model 

       18.7 Exact credibility 

19 Empirical Bayes parameter estimation 

       19.1 Introduction 

       19.2 Nonparametric estimation 

       19.3 Semi-parametric estimation

 

[Chapter 20 has a weight of 5% - 10% of the SOA Exam C]

PART VI SIMULATION 

20 Simulation 

       20.1 Basics of simulation 

       20.2 Simulation for specific distributions 

       20.3 Determining the sample size 

       20.4 Examples of simulation in actuarial modeling 

 

Calculators

Any approved calculator can be used for this class (approved list: http://www.soa.org/Education/Exam-Req/exam-day-info/edu-calculators.aspx). You may use more than one calculator on this list.  

 

Actuarial Examinations

In conjunction with M339J, M349P covers the content of SOA Exam C.  Students are expected to be familiar with survival, severity, frequency and aggregate models, and use statistical methods to estimate parameters of such models given sample data. Students are further expected to identify steps in the modeling process, understand the underlying assumptions implicit in each family of models, recognize which assumptions are applicable in a given business application, and appropriately adjust the models for impact of insurance coverage modifications.