Lecture 4
Video description: The lecture provides an overview of key linear algebra concepts such as eigenvalues, eigenvectors, matrix diagonalization, and singular value decomposition, emphasizing their applications in modeling dynamic systems and data analysis. It also introduces foundational probability theory concepts, including distributions, moments, covariance, principal component analysis, and their relevance to finance, portfolio management, and stochastic modeling.
Probability Theory Slides (PDF)
Probability Theory Applications Slides (PDF)
Suggested Readings:
- Lintner, John. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” The Review of Economics and Statistics 47, no. 1 (1965): 13–37. https://doi.org/10.2307/1924119
- Lintner, John. “Security Prices, Risk, and Maximal Gains From Diversification.” The Journal of Finance 20, no. 4 (1965): 587–615. https://doi.org/10.2307/2977249
See Problem Set 2, due one day after lecture 7
Lecture 5
Video description: Principal Components Analysis (PCA) is a statistical technique that transforms a random vector in a multidimensional space by shifting and rotating coordinates to identify orthogonal directions of maximum variability, often used in financial data to simplify complex covariance structures. Additionally, the discussion covers foundational probability concepts such as the Central Limit Theorem, utility optimization in asset pricing, and introduces stochastic processes like martingales, highlighting their importance in modeling financial markets and solving probability problems.
