Syllabus: M339J

A PROBABILITY MODELS WITH ACTUARIALS APPLICATIONS

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 M358K or M378K with a grade of at least C-.

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

[Chapters 3 – 9 have a combined weight of 15% - 20% of the SOA Exam C]

PART I INTRODUCTION

2 Random variables

2.1 Introduction

2.2 Key functions (cumulative distribution function, survival function, probability density function, probability mass function, and hazard rate (= force of mortality or failure rate)

3 Basic distributional quantities

3.1 Moments

3.2 Percentiles

3.3 Generating functions and sums of random variables

3.4 Tails of distributions

3.5 Measures of Risk

PART II ACTUARIAL MODELS

4 Characteristics of Actuarial Models

4.1 Introduction

4.2 The role of parameters

5 Continuous models

5.1 Introduction

5.2 Creating new distributions

5.3 Selected distributions and their relationships

5.4 The linear exponential family

6 Discrete distributions

6.1 Introduction

6.2 The Poisson distribution

6.3 The negative binomial distribution

6.4 The binomial distribution

6.5 The (a, b, 0) class

6.6 Truncation and modification at zero

7 Advanced discrete distributions  [Not Covered]

8 Frequency and severity with coverage modifications

8.1 Introduction

8.2 Deductibles

8.3 The loss elimination ratio and the effect of inflation for ordinary deductibles

8.4 Policy limits

8.5 Coinsurance, deductibles, and limits

8.6 The impact of deductibles on claim frequency

9 Aggregate loss models

9.1 Introduction

9.2 Model choices

9.3 The compound model for aggregate claims

9.4 Analytic results

9.5 Computing the aggregate claims distribution

9.6 The recursive method  [Exclude 9.6.1]

9.7 The impact of individual policy modifications on aggregate payments

9.8 The individual risk model

[Chapters 10 – 12 have a combined weight of 20% - 25% of the SOA Exam C]

PART III CONSTRUCTION OF EMPIRICAL MODELS

10 Review of mathematical statistics

10.1 Introduction

10.2 Point estimation

10.3 Interval estimation

10.4 Tests of hypotheses

11 Estimation for complete data

11.1 Introduction

11.2 The empirical distribution for complete, individual data

11.3 Empirical distributions for grouped data

12 Estimation for modified data

12.1 Point estimation

12.2 Means, variances, and interval estimation

12.3 Kernel density models

12.4 Approximations for large data sets

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 M349P, M339J 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.