0
MSc / P.G. Diploma
In
Financial Mathematics
at the
Department of Mathematics
Faculty of Engineering
of
University of Moratuwa
1
Master of Science / Post Graduate Diploma in Financial Mathematics
Document 1: Eligibility Requirements
(a). The degree of Bachelor of Science of Engineering of the University of Moratuwa,
or
(b). The degree of the Bachelor of Science of a recognized University with Mathematics,
Statistics or Computer Science as one of the main subjects,
or
(c).Any
other
special
degree
in
Mathematics,
Statistics,
Computer
Science
or
Management, the recognition of the degree to be judged by the Faculty and approved by
the Senate of University of Moratuwa.
or
(d). At least membership of a recognized professional institution in a relevant field and a
minimum of one year experience after obtaining a such membership, the acceptability of
the professional qualification of the candidate, the recognition of the institute and the
relevancy of the field for this purpose shall be judged by the Faculty and approved by
the Senate of University of Moratuwa.
2
Document 2 Course Curriculum and Scheme of Evaluation
MSc / Post graduate Diploma Course in Financial Mathematics Course Modules
Semester 1
Requirement: 40 credits are required for P.G. Diploma in Financial Mathematics
Compulsory Courses
Code
Core Module
Credits
Evaluation** %
Assignment
Exam
MA5100
Introduction to Statistics
4.0
20  10
80  20
MA 5101
Financial Mathematics Techniques
5.0
20  10
80  20
MA 5102
Operational Research Techniques 1
4.0
20  10
80  20
MA 5103
Information Technology for Finance &
Investment Analysis
4.0
20  10
80  20
Credits
Evaluation** %
Elective Courses
Code
Core Module
Assignment
Exam
MA5104
Mathematical Methods
4.0
20  10
80  20
MA 5105
Statistical Quality Control
3.0
20  10
80  20
MA 5106
Surveys of Sampling Techniques
3.0
20  10
80  20
Credits
Evaluation** %
Semester 2
Compulsory Courses
Code
Core Module
Assignment
Exam
MA5107
Actuarial Statistics
5.0
20  10
80  20
MA 5108
Information Management Systems
3.0
20  10
80  20
MA 5109
Financial Time Series Analysis &
5.0
20  10
80  20
4.0
20  10
80  20
Forecasting
MA 5110
Operational Research Techniques II
3
Elective Courses
Code
Core Module
Credits
Evaluation** %
Assignment
Exam
3.0
20  10
80  20
MA 5112
Design, Planning and Anlysis of
Experiments
Multivariate Analysis & Econometrics
4.0
20  10
80  20
MA 5113
Introduction to Marketing
3.0
20  10
80  20
Credits
Evaluation %
MA5111
Code
MA5114
**
Module
Dissertation
20.0
Assignment
Exam
Thesis
Viva
This evaluation scheme is the recommended one and can be changed within the range by the
Lecturer/Examiner provided that it is announced to the students at the beginning of the course
4
Document 3 : MSc / Post Graduate Diploma in Financial Mathematics Subject
Syllabi
1. MA 5100 Introduction to Statistics
Learning Objectives: The aim of this course is to provide students an introductory survey of
many business applications of descriptive and inferential statistics. This course prepares the
students to utilize probabilistic models in the analysis of managerial decision problems and uses
case study approaches. Theories learnt would be applied and analyzed in actual situations
related to problems in industry. It is also designed to acquaint the student with various ways of
summarizing distributions of populations and sample data and to show the relationship between
sample statistics and population parameters.
Out line of the syllabus:
Probability distribution theory with the emphasis on models and distributions associated with the
Poisson process. Introduction to decision theory, including decision trees utilities, expected value
of perfect and sample information.
A practical introduction to the techniques and methods of statistics. The course includes the
5
handling and description of numerical data, sampling and hypothesis testing, confidence
intervals, correlation and regression. Non-parametric methods. Many of the ideas will be
illustrated by use of the statistical computer package MINITAB.
2. MA 5101 Financial Mathematics Techniques
Learning Objectives: The purpose of this course in Financial Accountancy is to provide an
overview of the financial management issues and decisions involved in planning and managing
financial activities of the firm and view alternative ways of addressing these decisions.On
successful completion of this course, students will be able to define varying purposes of different
books, ledgers, and entries, and interpret less complex financial statements
Out line of the syllabus:
Forward Contracts, Future Contracts, Options, Types of Trades, Hedgers, Speculators , Onestep Binomial Models,
Risk Neutral valuation,
Two-Step Binomial Trees,
A put examples,
American options. The Markov property, Continuous time processes, The process for stock price,
The parameters, Ito’s lemma.
The Black-Schole-Merton model: Lognormal property of stock price, The distribution of the
rate return, The expected return,
Volatility,
differential equation, Risk neutral valuation,
Concept underlying Black-Schole-Merton
Black-Schole pricing formula.
Options of stock indices, currencies, and futures: Results for stock paying a known
dividend yield,
Options pricing formulas, Options on stock indices, Currency indices, Currency
options, Future options, evaluation of future options using a binomial tree, Black’s model for
valuing future’s options.
3. MA 5102 Operational Research Techniques 1
Learning Objectives: The objective of this course is to present scientific and mathematical
approaches to use when faced with day-to-day managerial decision problems, as well as specific
quantitative tools used to solve managerial problems. On successful completion of this course,
students will be able to apply different quantitative techniques and sensitivity analysis in
managerial decision making, using software in particular.
Out line of the syllabus:
Transportation and assignment algorithms, balanced and unbalanced transportation problems,
degeneracy, Hungarian method of assignment, transshipment problems. Network flows, maximal
flow, minimal flow, minimum spanning tree, and shortest path algorithm
in the network,
labeling technique, connection between network flow and transportation, matrix solution.
Inventory Control
4. MA 5103 Information Technology for Finance and Investment Analysis
6
Learning Objectives: The aim of this course is to provide an understanding of management
perspective of information systems, to provide basic understanding of the role of IT manager in
an
organizational
context,
and
the
ethical
and
legal
aspects
of
information
systems
management.
On successful completion of the course students will be able to describe and explain the strategic
importance of different information systems in an organizational setting and the different issues
that have to be considered when managing them in a cost effective way.
Out line of the syllabus:
Use of statistical software in computations, estimation, inference, and simulations. Functional
programming language of MATLAB and EXCEL Visual Basic. Applications of MATLAB in derivative
pricing and the application of Excel Visual Basic. Introduction to the theories of Artificial Neural
Networks (ANN), Group Method of Data Handling, Genetic Algorithms. Applications of AI
processes tools to pattern recognition and decision-making with special emphasis to areas such
as investments and credit rating classifications including data mining. Introduction of C++.
5. MA 5104 Mathematical Methods
Learning Objectives: The purpose of this course is to develop an awareness of the scope and
complexity of issues related to the Management of Technology. It will develop skills for critical
technology judgment and provide the student with principles and tools for technology evaluation
and management.
On successful completion of this course, students will be able to evaluate methods requirements
Out line of the syllabus:
Functions of several variables: Continuity, directional derivatives, differential of functions of one
variable, differentials of functions of several variables, the gradient vector, differentials of
composite functions and the chain rule,
the mean value theorem, Applications of partial
differentiation: Jacobians, the inverse function theorem, the implicit function theorem,
extremum problems.
Introduction to numerical analysis including the theory of finite differences, numerical integration
and differentiation, solution of initial valued ordinary differential equations, solution of simultaneous
linear algebraic equations by direct and iterative methods, solution of non-linear equations and
elementary ideas of curve fitting. Numerical solution of partial differential equations, Finite Element
Methods. Applications of MATLAB.
6. MA 5105 Statistical Quality Control
Learning Objectives: The benefits of improved quality and reduced costs associated with the
implementation of SPC have encouraged organizations to refine and extend their techniques
7
beyond those associated with traditional SPC. The conventional SPC techniques and, amongst
other things, enables participants to recognize situations requiring the use of more sophisticated
techniques apply the techniques effectively
Out line of the syllabus:
concepts of stable industrial processes. Systematic variation, random variation. SPC: variable &
attribute control charts,
X C, P,
CUSUM, charts. General ideas on economic designing of control
charts. Duncon’s model for the economic control chart. Capable process, capability &
performance indices. Estimation & confidence intervals for estimators of C p. Capability of series
system. Connection between proportion of defectives & Cp.
Acceptance Sampling plans:
Single, double & multiple sampling plans for attribute type. Operating characteristic functions &
other properties of the sampling plan. Use of sampling plans for rectification. Designing
&
sampling plan. Dodge-Romig acceptance sampling plans. Acceptance sampling plan for variables
with single & double specification limits. Designing variable acceptance sampling plans. AQL
based sampling plans. Continuous sampling plans.
7. MA 5106 Surveys of Sampling Techniques
Learning Objectives: Develop an understanding of alternative probability sample designs and
the statistical and practical factors that impact design choices Develop the ability to select an
estimator for a population parameter and an estimator of its variance, given a sample design
and auxiliary information (covariates) develop an understanding of the survey research process
from a scientific and practical perspective, and learn how statistical considerations interact with
the choice of data collection methods
Out line of the syllabus:
Basic methods of sample selection, simple random sampling with replacement, simple random
sampling without replacement, probability proportional sampling with and without replacement,
systematic sampling, estimation problems, Stratification: Allocation problems and estimation
problems, formation of strata and number of strata, method of collapsed strata. Cluster
sampling, multistage-sampling. Double sampling procedures, Ratio and regression estimators,
stratification.
8. MA 5107 Actuarial Statistics
Learning Objectives: This course introduces several of the major mathematical ideas
involved
present
in
calculating
valuation
of
life-insurance
future
income
premiums,
streams;
including:
probability
compound
distributions
interest
and
and
expected
values derived from life tables; the interpolation of probability distributions from values
estimated at one-year multiples; the `Law of Large Numbers' describing the regular
8
probabilistic behavior of large populations of independent individuals; and the detailed
calculation of expected present values arising in Insurance problems.
Out line of the syllabus: Section 1
Utility theory, insurance and utility theory, models for individual claims and their sums, survival
function, curate future lifetime, force of mortality. Life table and its relation with survival
function, examples, assumptions for fractional ages, some analytical laws of mortality, select
and ultimate tables. Multiple life functions, joint life and last survivor status, insurance and
annuity benefits through multiple life functions evaluation for special mortality
laws. Multiple
decrement models, deterministic and random survivorship groups, associated single decrement
tables, central rates of multiple decrement, net single premiums and their numerical
evaluations.
Distribution of aggregate claims, compound Poisson distribution and its applications. Distribution
of aggregate claims, compound Poisson distribution and its applications.
Section II – Insurance and Annuities
Principles of compound interest: Nominal and effective rates of interest and discount, force of
interest and discount, compound interest, accumulation factor, continuous compounding.
Life insurance: Insurance payable at the moment’s of death and at the end of the year of deathlevel benefit insurance, endowment insurance, differed insurance and varying benefit insurance,
recursions, commutation functions. Life annuities: Single payment, continuous life annuities,
discrete life annuities, life annuities with monthly payments, commutation functions, varying
annuities, recursions, complete annuities-immediate and apportion able annuities-due. Net
premiums: Continuous and discrete premiums, true monthly payment premiums, apportion able
premiums, commutation functions, and accumulation type benefits.
Payment premiums, apportion able premiums, commutation functions accumulation type
benefits.
Net premium reserves: Continuous and discrete net premium reserve, reserves on a semi
continuous basis, reserves based on true monthly premiums, reserves on an apportion able or
discounted continuous basis, reserves at fractional durations, allocations of loss to policy years,
recursive formulas and differential equations for reserves, commutation functions.
Some practical considerations: Premiums that include expenses-general expenses types of
expenses, per policy expenses.
Claim amount distributions, approximating the individual model, stop-loss insurance.
9. MA 5108 Information Systems Management
Learning Objectives:provide students with an in depth knowledge on human and technical
factors involved in systems analysis and design and the need for a structured approached to the
9
systems development process. Provide an understanding of management perspective of
information systems. Provide basic understanding of the role of IT manager in an organizational
context. To give an overview of ethical, legal aspects of information systems management
Out line of the syllabus:
Organizations and Information Systems, Information Systems Planning, Managing Information
and Supporting, Decision Makers, Information Systems Development, Enterprise Systems,
Outsourcing, Business Continuity Planning, Managing Operations, Services and Security,
Organizational Form and IT Architecture, Legal and Ethical Issues, and Overview of Electronic
Commerce and Mobile Computing.
10. MA 5109 Financial Time Series Analysis
Learning Objectives: The purpose of this course is to provide students with introductory tools
for the time series analysis of financial time series. This is a wide and rapidly growing field of
study so that it is not possible to provide more than an introductory treatment of the topics.
Students are encouraged to pursue further study in this area if they find that the topics covered
in this course are interesting.
Out line of the syllabus:
Definition and examples of time series, back-shift and differencing-operators, strong and weak
stationarity, definition of ACF, PACF.
Definitions and properties of the MA(q), MA(∞), AR(p), AR(∞) and ARMA(p, q), in particualr
their acf's, causal stationarity of AR, invertibility of MA models and causal stationarity and
invertibility of ARMA; concept of spectral density function and its applications; definition and
properties of integrated ARIMA(p, d, q) processes; definition and properties of random walks
with or without drift. Model selection following the AIC and BIC; brief introduction to linear
prediction and calculation of forecasting intervals for normal ARMA models; point and interval
forecasts for normal random walks with or without drift.
Definition and properties of the VAR (vector autoregressive) model, arrange a univariate time
series as a multivariate Markov model.
Nonlinear properties of financial time series; definition and properties of the well known ARCH,
GARCH etc. Cointegration in Single Equations, Modeling and Forecasting Financial Time Series.
11. MA 5110 Operational Research Techniques II
Learning Objectives: This course is an extension of Operations Research I and introduces
probabilistic models. This course is designed to show how probabilistic methods are applied to
managerial decision-making under certainty and uncertainty. The objective of this course is to
present different types of scientific and mathematical approaches for managerial decision making
with quantitative and modeling tools. Also, this emphasizes on applications in practice as well as
analytical models and problem solving with the use of computer software for problem solving.
10
On successful completion of this course, students will be able to transform managerial situations
into OR models, and apply the techniques learned under certain, probabilistic, and uncertain
situations.
Out line of the syllabus:
Revised simplex algorithm. Dual Simplex algorithm, sensitivity analysis and parametric
programming. Integer programming, Gomory's cutting plane, branch and bound, the knapsack
problem. Delayed column generation, the cutting stock problem.
Decision Theory: Introduction, Structuring the Decision Situations, Decision Making Under
Uncertainty, Decision Tree, Utility Theory.
Dynamic Programming: Introduction to Dynamic Programming under certainty and under
uncertainty, Infinite State Dynamic Programming.
Waiting Line Theory: Waiting Line Situations in Practical life, Arrival Distribution, Service
Distribution, Queue Discipline, introduction to Stochastic Processes, M/m/1, M/M/m Systems
with Finite & Infinite Population, An Introduction to other Queuing models and Queuing
networks.
Simulation and Stochastic Models: An introduction to stochastic processes and their
applications. Difference equations, Markov chains. Introduction to simulation.
12. MA 5111 Design, Planning and Analysis of Experiments
Learning Objectives: The purpose of this course is to teach the student to understand the
fundamentals of Design of Experiments (DOE) methodology. Software tools are commonly used
for DOE work. The convenience of these software tools has made it very easy to avoid learning
the fundamental concepts of DOE. The resulting oversight can cause experimental design errors,
produce meaningless data, and waste significant amounts of time and money. This course will
help the student choose the right software tool and DOE procedure for the job at hand.
Out line of the syllabus:
Randomization, replication, local control, one way and two way classification with unequal and
equal number of observations per cell (with / without interactions). Connectedness, balance,
orthogonality, BIBD, ANOCOVA.
2 k Full factorial experiments:
diagramatic presentation of main effects and first order
interactions, model, analysis of single as well as more than one replicates, using ANOVA.
Total confounding of 2
k
design in 2
p
3
blocks, p 2. . Partial confounding in 2
p
blocks, p =2, 3.
Fractional factorial experiments, statistical analysis of 32 design. Random effect models for one
way classification.
11
13. MA5112
Multivariate Analysis & Econometrics
Learning Objectives: This course focuses on the application of multivariate statistical methods
in a research environment. The topics include multivariate linear modeling techniques such as
MANOVA, multivariate regression, discriminant function analysis, and canonical correlation
analysis; multivariate models for repeated measures analysis; dimension reduction techniques
such as principal components analysis; exploratory factor analysis; and analysis of structure
including confirmatory factor analysis and structural equation modeling techniques. The course
concludes with a chapter about multivariate data preparation and assumptions checking.
Out line of the syllabus:
Multivariate Normal distribution, pdf and mgf, singular and nonsingular normal distributions,
distribution of a linear form and a quadratic form of normal variables, marginal and conditional
distributions. Multiple regression and multiple and partial correlation coefficients. Definition and
Relationships.
MLE's of the parameters of multivariate normal distribution and their sampling distributions
Tests of hypothesis about the mean vector of a multinormal population. Introduction to Principle
Components and canonical correlation coefficients and canonical variables. Cluster Analysis.
Classification problem. Discriminant analysis, Mahalanobis. Methods and applications of MANOVA
Econometrics:
Simple and multiple regression analysis; test statistics, problems of multicollinearity and
misspecification;
transformation
of
variables,
dummy
variables,
proxy
variables;
serial
correlation, heterosedacity; measurement errors and the Permanent Income Hypothesis;
simultaneous equation bias, indirect least squares, instrumental variables estimation, two stage
least squares; model evaluation.
14.MA5113 Introduction to Marketing
Learning Objectives: This course introduces students to the principles and practices of
marketing and marketing management within a business context. Topics include the broad
headings of marketing and the marketing process, developing marketing opportunities and
strategies, competition, the marketing mix, pricing, and managed marketing. Class discussions
will involve the application of theoretical concepts to the environment in which the marketing
managers operate. Emphasis is placed on the application of concepts to the real marketing
situations. Particular attention will be given to the application of modern skills and techniques to
marketing management through case studies.
Out line of the syllabus:
The role of marketing at the corporate and business level.
Marketing information and marketing research: marketing intelligence, marketing research
process, junctions, design and analysis of market survey, application of analytical techniques
12
and computer software.
Analyzing the marketing environment. Consumer markets and buyer behavior. Industrial
markets and organizational buyer behavior. Market segmentation, targeting and positioning.
New product development. Managing the product line. Selecting and managing marketing
channels. The design of marketing communication and sales promotion. Marketing services.
International marketing. Organization implementation and control of marketing programs
Document 4: Performance Criteria for P.G. Diploma in Financial Mathematics
4.1. Title of award
Post-Graduate Diploma in Financial Mathematics
4.2. Participation in the Academic Programme
4.2.1 At least 80% attendance is normally required in lectures and tutorials to be
eligible to sit for the examination.
4.2.2 Participation is compulsory in seminars, and assignments.
4.3. Pass in the Post Graduate Diploma
4.3.1 A candidate is deemed to have passed the postgraduate Diploma if he/she has:
(a). Obtained a minimum of 40 credits offered according to the course curriculum
approved by the Faculty and Senate, by successfully completing the continuous
assessment components and the written examinations.
(b). If the candidate is unsuccessful in any of the parts (a) he/she may be re-examined.
13
Normally, only one re-examination will be allowed and this will be at the next holding of
the examination(s)/assessments(s). No postponement will be allowed without prior
approval of the Senate.
Note Where the overall mark for a module consists of a written examination mark as
well as marks for continuous assessments of that module, the candidate shall obtain at
least 40% of marks assigned for each component.
4.3.2
Classes will not be awarded.
4.3.3 Credit Rating
One credit corresponds to approximately 14 hours of lectures or 28 hours of
assignments.
4.4. Award of Grades for Subject Modules
Grades of performance for the modules shall be awarded as follows
* Guideline
Grade
Percentage
Grade
Description
point
85 and above
A+
4.2
75 to 84
A
4.0
70 to 74
A-
3.7
65 to 69
B+
3.3
60 to 64
B
3.0
55 to 59
B-
2.7
50 to 54
C+
2.3
Pass
I
0.0
Incomplete
F
0.0
Fail
N
0.0
Academic Concession
Excellent
Good
* The examiner and the moderator may change the grade boundaries within reasonable limits if
they feel that justifiable grounds exist for such changes.
4.4.1 Grade C+ or above is required to pass a module and earn credits for the module.
14
4.4.2 A student who has not obtained a grade C+ in a module but has obtained minimum
marks for at least one component, receives an incomplete grade I.
4.4.3 A candidate receiving an F grade must repeat all components.
4.4.4 The I grade or F grade can be improved to a C+ grade by repeating one or more
components to satisfy the requirements for a pass in the module. The . maximum grade
awarded for a module after repeating one or more components will be a C+ and will be
used for calculating the Grade Point Average.
4.4.5 Grade N signifies Academic Concession granted with the approval of the Faculty,
in the event a student is unable to sit for the end-of-semester examination due to
illness or other compelling reasons. In such instances the student must notify the
Registrar within 48 hours of the cause. Further, the student should make an appeal
with supporting documents to the Dean for an Academic Concession within one week
from the date of the end of the examination. The continuous assessment component
can be carried forward to the next examination as the first attempt.
4.5 Calculation of the grade point average :
The grade point average (GPA) is calculated from the grade points received by the student
(grade point) and the credit assigned for each of the modules (credits) by the formulae.
GPA 
 (Grade po int  Credits )
 Credits
4.6 Date of Award:
The effective date of the P.G. Diploma shall be the first day of the following month after
successful completion of all of the following :
(a). written examinations
(b). seminars
(c). assignments
4.7 Duration of the Course:
All lectures, assignments and seminars will be normally completed in 15 months.
Examinations in the relevant subjects will be conducted within this period.
15
Document 5: Performance Criteria - Master of Science in Financial Mathematics (By
Course)
5.1. Title of award
Master of Science in Financial Mathematics
5.2. Participation in the Academic Programme
5.2.1 (a). Passed the postgraduate examination as specified in clause 4.3.1 but has not been
awarded the Postgraduate Diploma
And (b). Has obtained an overall GPA as decided by the Department subject to maximum cutoff
3.0 and minimum cutoff 2.5 at the Postgraduate examination.
And (c). Undertake an individual research dissertation, as assigned by the Department, on a
specific subject area, for a period of not less than 9 months duration on a part time basis or
equivalent.
(d). The postponement of the dissertation will only be allowed with prior approval from the
Senate.
5.3. Evaluation of the Research Project
5.6.1 A candidate must undertake an individual research project as assigned by the
Department on a specific area.
5.6.2 In order to pass the Research project, a grade of at least C + must be obtained.
16
5.6.3 All pass grade carry 20 credits for the research project.
5.4. Award of MSc Degree
(a).
Passed the Postgraduate Examination as specified in clause 4.3.1
AND
(b).
Successfully completed any additional prescribed seminars and assignments
AND
(c).
Successfully completed the research dissertation assigned to the candidate.
5.5 Date of award
The effective date of the M.Sc degree shall be the first day of the following month after the
successful completion of all of the following:
(a) written examination(s)
(b) assignment(s)
(c) seminars
(d) examination of the
project and oral examination.
5.6. Duration of Course
All lectures, assignments and seminars etc will be normally completed in 15 months. A
project of 9 months duration has to be done by each student after completion of
requirements of (a ), (b) and (c)
Document6
of section 5.4.
Details of the Resources Personnel
From University of Moratuwa
Mr.T.M.J.A.Cooray (Course Coodnaor)
Bsc (Pera),P.G.Diploma(pera), MSc(Col). MPhil(Mora)
Dr. G.T.F.de Siva
Bsc (London),BSc(Cey), MPhil(London), DIC, CEng, MBCS
Dr. M.Z.M.Malhardeen Bsc (Cey), PhD(Heriot Watt)
Dr. H.S.C.Perera Bsc Eng(Mora), MEng(AIT), DEng(AIT)
Dr. T.S.G. Peiris Bsc(Col), Mphil, PhD(SL)
Mr. U.C.Jayatilake Bsc Eng (Mora), MSc(Mora)
Mrs. Sherin Ahamed Bsc(Pera), M.Eng(Japan), MSc(PGIA)
Mr. Mohommad Firdhous Bsc Eng, MSc, MBA(SL), MIET(London), CCNA
Note*:
Dr. S.P.C.Perera BSc.Eng. (Pera) M.Sc,PhD(Texas Tech,USA)
Senior Lecturer
Dept. Engineering Mathematics
Faculty of Engineering
Univ: Peradeniya.
17
Mr. Rohana Disanayaka Bsc(colombo), MSc (Punai)
Senior Lecturer, Dept of Mathematics
Sir John Kothalawala Defence Academy
Ratmalana.
Mr. Keerthi Peiris Bsc(Mgt), MBA(Colombo)
International Marketing Manager
Maliban Biscuits Associates Ltd,