## 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

18.5 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.