# Math 178C: General Course Outline

## Course Description

178C. Foundations of Actuarial Mathematics: Loss models. (4). Lecture, three hours; discussion, one hour. Requisite: 178B. This course is the third of the three quarter sequence 178ABC. 178C studies loss models associated with actuarial problems. It covers severity, frequency, and aggregate loss models, parameter estimation (frequentist, Bayesian), model selection and credibility. Letter grading.

## Course Information:

The three quarter sequence 178ABC is the actuarial core of the FAM major. 178C covers topics associated with short term actuarial risk. With 178B, most of the topics 1-7 on the SOA STAM exam are covered.

## Textbook(s)

S. Klugman, H. Panjer, G. Willmot, Loss Models: From Data to Decisions. 3rd Edition, Wiley, 2012.
Hardy, Mary R., Long-Term Actuarial Mathematics Study Note. Society of Actuaries, 2017.
Education and Examination Committee of the Society of Actuaries - Long Term Actuarial Mathematics Supplementary Note.
https://www.soa.org/Files/Edu/2018/2018-ltam-loss-models.pdf

## Schedule of Lectures

Lecture Section Topics

1

KPW 8.1-8.2

Deductibles

2

KPW 8.3-8.4

Loss elimination ratio, policy limits

3

KPW 8.5-8.6

Coinsurance, deductibles, limits, impact of deductibles on claim frequency

4

KPW 9.1-9.2

Introduction to aggregate loss models and model choice

5

KPW 9.3

Compound model

6

KPW 9.3

Continued and examples.

7

KPW 9.4

Other closed form results

8

KPW 9.5, 9.6-9.6.5 (exclude 9.6.1)

Recursive method, arithmetic discretization

9

KPW 9.7-9.8.2

Effect of modifications and individual risk model

10

Empirical distributions, grouped data

11

Right censored data

12

Left truncated data

13

Approximations for large data sets

14

Maximum likelihood estimation of decrement probabilities

15

Estimation of transition intensities

16

Review/Leeway

17

Midterm

18

KPW 13.2

Maximum likelihood estimation

19

KPW 13.4

Non-normal confidence intervals and exercises

20

KPW 14.1-14.2

Frequentist estimation: Poisson and negative binomial cases

21

KPW 14.3, 14.4, 14.6

Binomial and (a, b,1) cases and effect of exposure

22

KPW 15.1

Bayes? Theorem

23

KPW 15.2

Bayesian inference and prediction

24

KPW 15.3

Conjugate priors

25

KPW 16.1-16.3

Model selection: introductory concepts

26

KPW 16.4 (except 16.4.2)

Hypothesis testing

27

KPW 16.5

Selecting a model

28

KPW 17.1-17.5

Classical Credibility

29

KPW 18.2

Conditional Distributions

30