# Math 178A: General Course Outline

## Course Description

178A. Foundations of Actuarial Mathematics: Life Insurance and Annuities. (4). Lecture, three hours; discussion, one hour. Requisite: course 32B, 175 or 177, 170A or 170E or Statistics 100A. An introductory course on to the mathematics associated with long term insurance coverages. Single and multiple life survival models, annuities, premium calculations and policy values, reserves, pension plans and retirement benefits. Letter grading.

## Course Information:

A core sequence course for the Financial Actuarial Mathematics major, Mathematics 178A and the first half of Mathematics 178B cover the syllabus of the Society of Actuaries (SOA) Long-Term Actuarial Mathematics (LTAM) exam. By the end of this course, students will be able to value and set premiums for insurance instruments of numerous types using traditional actuarial models. They will also understand the typical models of life contingencies which are used in the calculations.

## Textbook(s)

Dickson, David C.M., Hardy, Mary R. and Waters, Howard R, Actuarial Mathematics for Life Contingent Risks. 2nd ed., Cambridge University Press, 2013.

## Schedule of Lectures

Lecture Section Topics

1

1

Life insurance and annuity contracts, pension benefits, mutual and proprietary insurers.

2

2.2

3

2.3

Force of mortality.

4

2.4-2.5

First actuarial notation and basic properties of TX.

5

2.6-2.7

Curtate future lifetime, further discussion and exercises.

6

3.1-3.3.1

Life tables, fractional age assumptions.

7

3.3.2-3.6

National life tables, survival models for life insurance holders, survival models for life insurance, life insurance underwriting.

8

3.7-3.9

Select and ultimate survival models, select life tables.

9

3.10-3.13

Heterogeneity in mortality, mortality trends and sample problems.

10

4.1-4.4.3

Whole life insurance (continuous, annual, 1/m-thly case).

11

4.4.4-4.4.7

Recursions, term insurance, pure endowment and endowment insurance.

12

4.4.8-4.5.2

Deferred insurance benefits, uniform distribution of deaths assumption, claims acceleration approach.

13

4.6-4.8

Pure endowment, endowment insurance, deferred insurance benefits.

14

15

Midterm

16

5.1-5.4.2

Whole life annuity due and term life annuity.

17

5.4.3-5.7

Whole life immediate, term life immediate, whole life continuous, term continuous, payable 1/ m-thly cases, comparison by payment frequency.

18

5.5-5.10

Deferred, guaranteed, increasing cases.

19

5.11-5.14

Evaluating annuity functions, recursions, applying UDD assumption, Woolhouse?s formula.

20

6.1-6.4

Present value of future loss random variable.

21

6.5-6.6

22

6.7

Profit

23

6.8-6.10

Portfolio percentile maximum principle, extra risks.

24

7.1-7.3.1

Policies with annual cash flows, future loss random variable.

25

7.3.2

Case of policies with annual cash flows.

26

7.3.3

Recursive formulas for policy values.

27

7.3.4, 7.4

Annual profit by source, case of policies with cash flows at 1/m-thly.

28

7.5

Case of continuous cash flows.

29

7.8-7.10

Negative policy values, deferred acquisition expenses and modified premium reserves, net premium approach.

30

Leeway/Review.