MATH3804 Syllabus

COURSE NAME: ACTUARIAL MATHEMATICS II
COURSE CODE: MATH3804

LEVEL: III
SEMESTER: I
NUMBER OF CREDITS: 3
PREREQUISITES:
Mathematics of Finance (MATH2210), Introduction to Actuarial Mathematics (MATH2220)
RATIONALE
This course is an extension and expansion of that for Introduction to Actuarial Mathematics. The
goal of the syllabus is to provide an understanding of fundamental mathematical techniques
required to value and model cash flows dependent on death, survival, disability, termination,
sickness and other uncertain events. It also covers multiple life and other types of status.
COURSE DESCRIPTION:
This is a compulsory level III course which is an important foundation course in actuarial science.
Candidates should master the fundamental concepts of actuarial and financial mathematics and its simple
applications as indicated in the Learning outcomes. This course allows the candidate to begin
preparation for the professional examinations (the Society of Actuaries Actuarial Models examination,
Exam 3 of the Casualty Actuarial Society, and the Faculty/Institute of Actuaries Contingencies
examination).

LEARNING OUTCOMES
On completion of this course the student should be able to:
Calculate the reserves for life insurance and annuity contracts based on single and
multiple decrement tables using the Prospective and Retrospective Methods.
Calculate premiums for all types of policies based on the multiple decrement tables and
single life table (SDT)
Be able to construct a Multiple Decrement Table (MDT) and its Associated Single
Decrement Tables (ASDT).
Carry out calculations based on both the SDT and the MDT.
Do all types of problems based on joint life, multiple life, last survivor statuses.
Carry out calculations for Reversionary Annuities.
Understand and be able to do calculations using the Common Shock Model.
Understand continuous-time Markov chain models, discrete approximations of
continuous-time Markov chain models and discrete-time Markov chain models
CONTENT
Reserves
Based on Single Decrement (Life) Table: Calculation of Reserves using Prospective and Retrospective
methods, Recursive Formula, Policy Alteration

Joint Life Functions

Study of T(x) and T (y), the complete future lifetimes of two lives (x) and (y), Joint Cumulative
Function, Joint Density Function, Joint survival function, Covariance of T(x) and T (y),
Correlation coefficient of T(x) and T(y), Marginal distributions of T(x) and T(y)

Study of the Joint Status (xy) and Last Survivor

Definition of joint status (x y) and Last Status Survivor xy , Full study of T (x y) including and
T xy , Cumulative Distribution Function, Probability Density Function, Expectation, Variance,
Survival Function, Probabilities associated with T(xy) and T xy , Force of failure of the status
(xy) and status xy

Insurances and Annuities

Problems on Insurances and Annuities based on Joint Life status and Last survivor status,
Problems on Reversionary Annuities

The Common Shock Model
Definitions, Modelling Dependence, Applications to all types of Insurance and Annuity
Problems
MDT and ASDT
Definitions, Complete study of MDT, Complete study of ASDT, Construction of MDT from
ASDT and vice versa, Incorporating continuous and discrete decrements, Problems involving
MDT and ASDT, Applications to Pensions Annuities and Insurances.
Markov Chain Models

Calculate the probability of being in a particular state and transitioning between states based on
continuous-time Markov chain models, discrete approximations of continuous-time Markov
chain models and discrete-time Markov chain models.

Calculate present values of cash flows by redefining the present-value-of-benefits and present-
value-of-premium random variables to Markov chain models.

Calculate benefit reserves and premiums using a Markov chain model with specified cash flows.

TEACHING METHODOLOGY:
This course will be delivered by a combination of theoretical classes, practices (tutorials) and
other group activities. The delivery mode will be largely interactive. The total estimated 39
contact hours are broken down as follows: 28 hours of lectures and 11 hours of tutorials. The
course material (complimentary notes, practice problems and assignments) will be posted on
ourvle http://ourvle.mona.uwi.edu/

ASSESSMENT:

The course assessment will be divided into two components: a coursework component worth
25% and a final exam worth 75%.

One coursework exam worth 25% of the final grade
The final exam will be two hours in length and consist of compulsory questions.

REFERENCE MATERIAL
Prescribed Text:
Bowers, N.L. et al, Actuarial Mathematics (Second Edition), 1997, Society of Actuaries

Highly Recommended Text:
Cunningham, R. Herzog, T., Moels for Quantifying Risk (Thir Edition), 2009, Actex Publications

Online resources:
The following are free online lectures which the student may access for revision purposes:
http://www.soa.org/files/pdf/edu-2008-spring-mlc-24-2nd.pdf
http://www.actuarialseminars.com/Misc/SNorderform.html

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COURSE NAME: ACTUARIAL MATHEMATICS II

COURSE CODE: MATH3804

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