Course No.
Title of the Course
Course Structure
Pre-Requisite
EIMTC04/ ITMTC04/
INMTC04
Optimization Principles
and Techniques
L-T-P
3-1-0
Mathematics-I
FCMT001
COURSE OUTCOMES:
1. Understanding the real life application, formulation and solution procedure for Linear programs.
2. Understanding the duality theory of linear programs and Transportation and Assignment Problems.
3. Understanding the basics of Game theory and its solution from Linear program.
4. Understanding the real life application, formulation and solution procedure for Integer programs.
5. Learning of the gradient based KKT optimal conditions for non-linear programming problems.
COURSE CONTENT :
UNIT-I: Linear Programming: Introduction to the optimization problems, Introduction and formulation of the
linear programming problem, geometry of linear programming problems, simplex algorithm in LPP.
UNIT-II: Duality theory, and special LPP: Introduction and interpretation of dual of LPP, Important relations
between the solution of LPP and its dual, dual simplex method, Complementarity slackness theorem,
Introduction to the transportation and assignment problems, solution algorithms of transportation and
assignment problem.
UNIT-III: Game theory: Introduction to the Game theory, Two person zero-sum game, Saddle points, Solution
methods of games without saddle point: Randomized strategies, Domination, and Graphical method, Linear
programming and zero sum game.
UNIT-IV: Integer Programming problem: Introduction and formulation to the Integer programming problem,
Gomery’s method for all integer programming problems, mixed integer programming problems.
UNIT-V: Non-linear Optimization problems
Introduction to the non-linear optimization, convex/concave functions and their properties, optimality conditions
for unconstraint optimization problem, method of Lagrange multipliers for constraint optimization problem,
Karush-Kuhn-Tucker optimality conditions, basic constraint qualification, Convex optimization and quadratic
programming.
Text book:
1. S. Chandra, Jayadeva, A. Mehra, Numerical Optimization with Applications, 1 st Edition, Narosa
Publishing House, 2009.
Reference Books:
1. Singiresu S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, 4th edition,
2009.
2. Edwin K. P. Chong, Stanislaw H. Zak, An Introduction to Optimization, Wiley, 3 rd edition, 2011.
3. H. S. Kasene & K. D. Kumar, Introductory Operations Research, Springer (India), Pvt. Ltd., 2004
4. George Bernard Dantzig, Mukund Narain Thapa, “Linear programming”, Springer series in operations
research 3rd edition, 2003.
5. H. A. Taha, “Operations Research: An Introduction”, 8th Edition, Pearson/Prentice Hall, 2007.
6. Kalyanmoy Deb, “Optimization for Engineering Design – Algorithms and Examples”, PHI Learning
Pvt. Ltd, New Delhi, 2005.
7. S. K. Mishra, Bhagwat R., Introduction to Unconstrained Optimization with R, Springer, 2019.
8. S. K. Mishra, Bhagwat R., Introduction to Linear program with MATLAB, Springer, 2017.
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** EIMTC04: ECE (EIOT; main campus)
ITMTC04: Information technology (main campus)
INMTC04: Information technology (ITNS; main campus)
Course No.
Title of the Course (Core Course)
CMMTC17 Financial Engineering
Course
Structure
3L-1T-0P
Pre-Requisite
CMMTC11
(Scientific Computing)
COURSE OUTCOMES (CO): After successful completion of course, students will be able to
1. Know the basics of financial mathematics, financial markets, and financial instruments.
2. Understand the concepts of interest rates and bonds.
3. Understand the option pricing in the framework of discrete time
4. Understand the option pricing in the framework of continuous time
5. Understand and formulate the portfolio optimization models.
COURSE CONTENT:
UNIT I: Introduction to financial instruments, interest rates and pricing of bonds: Introduction of financial
system, financial markets, and financial instruments: stocks, bonds, derivatives, mutual funds; Interest rates, time
value of money, present and future values of cash flow streams; Bonds and bonds pricing, yield, duration and
convexity term structure of interest rates.
UNIT II: Option pricing I: Introduction to derivatives, Hedging, no-arbitrage principle, forward and futures
contracts and their pricing with and without dividends, hedging strategies using futures; Call and put options,
hedging strategies involving options, Pay-off curves of options combinations, single and multi period binomial
lattice models for European and American options pricings, existence of risk neutral probabilities, options on
dividend paying stock.
UNIT III: Option pricing II: The Cox-Ross-Rubinstein (CRR) formula, Black-Scholes option pricing formula.
UNIT IV: Portfolio optimization I: Expected value and variance of a random variable, Mean-variance portfolio
optimization (Markowitz model), solving the Markowitz model using real life stock price data.
UNIT V: Portfolio optimization II: Mean absolute deviation (MAD) based portfolio optimization, Minimax
rule based portfolio optimization, Introduction and calculation of Value-at-Risk (VaR) of an asset and
Conditional Value-at-Risk (CVaR) of an asset.
Text book:
1. S. Chandra, S. Dharmaraja, A. Mehra, R. Khemchandani , Financial Mathematics: An Introduction,
Alpha Science International Ltd.
SUGGESTED READINGS:
1. M. Capinski and T. Zastawniak (2003), Mathematics for Finance: An Introduction to Financial
Engineering and Springer-Verlar, London
2. D. G. Luenberger (1998), Investment Science, Oxford University Press, New York.
3. J. C. Hull (2000), Options, Futures and other Derivatives, Fourth edition , Prentice Hall Inc.,
Upper Saddle River.
4. R. J. Elliott and P. E. Kopp, Mathematics of Financial Markets, Springer, 1999.
5. M. Bartholomew-Biggs, Nonlinear optimization with financial applications, Springer Science &
Business Media, 2005.
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