Algebra

Problem set for graduate students to practice implementing Monte Carlo simulations, calculating standard error, and understanding variance reduction techniques.

Graduate-level slides covering Monte Carlo methods, Geometric Brownian Motion paths, and the Law of Large Numbers applied to derivative pricing.

Problem set for graduate students to practice calculating VaR and Expected Shortfall, analyzing the impact of non-normal distributions on risk metrics.

Graduate-level slides covering VaR, Expected Shortfall, tail risk metrics, and the limitations of normal distributions.

Problem set for graduate students to price European options using the binomial model and calculate delta-hedging portfolios.

Graduate-level slides covering risk-neutral measures, the fundamental theorem of asset pricing, and the derivation of the binomial model.

Problem set for graduate students to compute portfolio expected returns and variance using matrix algebra, and derive the Minimum Variance Portfolio.

Graduate-level slides covering portfolio expected returns, covariance matrices, and the formulation of the Markowitz mean-variance optimization problem.

Problem set for graduate students to practice calculating expected utility, risk premiums, and deriving risk aversion measures.

Graduate-level slides covering the St. Petersburg Paradox, vNM Utility functions, and risk premiums in quantitative finance.

Assessment rubric for the Algorithmic Implementation Challenge, evaluating correctness, robustness, analysis, and code quality.

Instructions for the culminating project where students implement and compare Gradient Descent and BFGS algorithms on a black-box function.

Case study worksheet for Lesson 5 focusing on deriving the dual function, solving the dual problem, and verifying strong duality and saddle point conditions.

The final project guide for students, applying KKT conditions to a logistics network problem and requiring economic interpretation of shadow prices for business strategy.

Visual presentation for Lesson 5 covering the Lagrangian, primal and dual problems, weak/strong duality, and saddle point conditions.

Case-study worksheet where students analyze the impact of momentum and stochastic noise on navigating local minima and saddle points.

A teacher guide for the final project in operations research, providing network flow formulation strategies and a grading rubric for dual interpretation.

Techniques for navigating non-convex objective functions, including strategies to escape local minima and handle saddle points using momentum and stochastic methods.

Slides for the final lesson on operations research, applying constrained optimization to supply chain, capacity, and demand problems.

Problem set for Lesson 4 focusing on calculating Hessians, classifying critical points using eigenvalues, and applying Sylvester's Criterion for global convexity.