1
MSc / P.G. Diploma
In
Financial Mathematics
at the
Department of Mathematics
Faculty of Engineering
of
University of Moratuwa
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.
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 / /
MA 5101 / Financial Mathematics Techniques / 5.0 / /
MA 5102 / Operational Research Techniques 1 / 4.0 / /
MA 5103 / Information Technology for Finance & Investment Analysis / 4.0 / /
Elective Courses
Code / Core Module / Credits / Evaluation** %Assignment / Exam
MA5104 / Mathematical Methods / 4.0 / /
MA 5105 / Statistical Quality Control / 3.0 / /
MA 5106 / Surveys of Sampling Techniques / 3.0 / /
Semester 2
Compulsory Courses
Code / Core Module / Credits / Evaluation** %Assignment / Exam
MA5107 / Actuarial Statistics / 5.0 / /
MA 5108 / Information Management Systems / 3.0 / /
MA 5109 / Financial Time Series Analysis & Forecasting / 5.0 / /
MA 5110 / Operational Research Techniques II / 4.0 / /
Elective Courses
Code / Core Module / Credits / Evaluation** %Assignment / Exam
MA5111 / Design, Planning and Anlysis of Experiments / 3.0 / /
MA 5112 / Multivariate Analysis & Econometrics / 4.0 / /
MA 5113 / Introduction to Marketing / 3.0 / /
Code / Module / Credits / Evaluation%
Assignment / Exam
MA5114 / Dissertation / 20.0 / 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
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 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 ,One-step 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, Concept underlying Black-Schole-Merton differential equation, Risk neutral valuation, 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
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 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, 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 Cp. 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 in calculating life-insurance premiums, including: compound interest and
present valuation of future income streams; probability distributions 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
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 death-level 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 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 5109Financial 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 and 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 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.
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.
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 design in blocks, . Partial confounding in blocks, p =2, 3. Fractional factorial experiments, statistical analysis of 32 design. Random effect models for one way classification.