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 17 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., LongTerm 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/2018/2018ltamlossmodels.pdf
Schedule of Lectures
Lecture  Section  Topics 

1 
KPW 8.18.2 
Deductibles 
2 
KPW 8.38.4 
Loss elimination ratio, policy limits 
3 
KPW 8.58.6 
Coinsurance, deductibles, limits, impact of deductibles on claim frequency 
4 
KPW 9.19.2 
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, 9.69.6.5 (exclude 9.6.1) 
Recursive method, arithmetic discretization 
9 
KPW 9.79.8.2 
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 
Nonnormal confidence intervals and exercises 
20 
KPW 14.114.2 
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 16.116.3 
Model selection: introductory concepts 
26 
KPW 16.4 (except 16.4.2) 
Hypothesis testing 
27 
KPW 16.5 
Selecting a model 
28 
KPW 17.117.5 
Classical Credibility 
29 
KPW 18.2 
Conditional Distributions 
30 