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
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
14.2 Negative 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
16.2 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
17.2 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
18.2 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
19.2 Nonparametric estimation
19.3 Semi-parametric estimation
[Chapter 20 has a weight of 5% - 10% of the SOA Exam C]
PART VI SIMULATION
20.1 Basics of simulation
20.2 Simulation for specific distributions
20.3 Determining the sample size
20.4 Examples of simulation in actuarial modeling
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.
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.