Mathematical Portfolio Theory
About Course
This Mathematical Portfolio Theory course will give an introduction to the mathematical approaches used for the design and analysis of financial portfolios.
It would be useful to participants who want to get a basic insight into mathematical portfolio theory, as well as those who are looking at a career in the finance industry, particularly as asset managers. The course would be accessible to a broad spectrum of students of Mathematics, Statistics, Engineering, and Management (with the requisite background in Mathematics). Further, practitioners in the finance industry would also find the course useful from a professional point of view.
INTENDED AUDIENCE: Advanced undergraduate as well as postgraduate students in Mathematics, Statistics, Engineering, and Management (with requisite background in Mathematics).
Course Content
Mathematical Portfolio Theory

Mathematical Portfolio Theory [Intro Video]
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Lec 1: Probability space and their properties, Random variables
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Lec 2: Mean, variance, covariance and their properties
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Lec 3: Linear regression; Binomial and normal distribution; Central Limit Theorem
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Lec 4: Financial markets
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Lec 5: Bonds and stocks
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Lec 6: Binomial and geometric Brownian motion (gBm) asset pricing models
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Lec 7: Expected return, risk and covariance of returns
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Lec 8: Expected return and risk of a portfolio; Minimum variance portfolio
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Lec 9: Multiasset portfolio and Efficient frontier
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Lec 10 : Capital Market Line and Derivation of efficient frontier
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Lec 11 : Capital Asset Pricing Model and Single index model
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Lec 12: Portfolio performance analysis
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Lec 13: Utility functions and expected utility
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Lec 14: Risk preferences of investors
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Lec 15: Absolute Risk Aversion and Relative Risk Aversion
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Lec 16 : Portfolio theory with utility functions
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Lec 17: Geometric Mean Return and Roy’s SafetyFirst Criterion
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Lec 18: Kataoka’s SafetyFirst Criterion and Telser’s SafetyFirst Criterion
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Lec 19: Semivariance framework
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Lec 20: Stochastic dominance; First order stochastic dominance
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Lec 21: Second order stochastic dominance and Third order stochastic dominance
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Lec 22: Discrete time model and utility function
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Lec 23: Optimal portfolio for singleperiod discrete time model
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Lec 24: Optimal portfolio for multiperiod discrete time model; Discrete Dynamic Programming
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Lec 25: Continuous time model; HamiltonJacobiBellman PDE
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Lec 26: HamiltonJacobiBellman PDE; Duality/Martingale Approach
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Lec 27: Duality/Martingale Approach in Discrete and Continuous Time
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Lec 28: Interest rates and bonds; Duration
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Lec 29: Duration; Immunization
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Lec 30: Convexity; Hedging and Immunization
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Lec 31: Quantiles and their properties
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Lec 32: Value – at – Risk and its properties
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Lec 33: Average ValueatRisk and its properties
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Lec 34: Asset allocation
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Lec 35: Portfolio optimization
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Lec 36: Portfolio optimization with constraints, ValueatRisk: Estimation and backtesting
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