Microeconomic Consumer Theory

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Asset Pricing and Hedging in Complete Markets

Covers asset pricing, hedging, American claims, stopping times, and dynamic programming in finance.

Convex Sets: Mathematical Optimization

Introduces convex optimization, covering convex sets, solution concepts, and efficient numerical methods in mathematical optimization.

Convex Optimization: Exercises

Covers exercises on convex optimization, focusing on formulating and solving optimization problems using YALMIP and solvers like GUROBI and MOSEK.

Primal-dual optimization: Theory and Computation

Explores primal-dual optimization, conjugation of functions, strong duality, and quadratic penalty methods in data mathematics.

Optimisation Algorithms: Greedy Approach

Explores optimization problems solved with greedy algorithms and proves the optimality of the Cashier's Algorithm for U.S. coins.

Lagrangian Duality: Convex Optimization

Explores Lagrangian duality in convex optimization, transforming problems into min-max formulations and discussing the significance of dual solutions.

Power System Economics Fundamentals

Explores power system economics, Nash equilibrium points, profit maximization, and system security.

Optimization Problems: Lagrange Multiplier Equations

Introduces the Lagrange multiplier method for solving optimization problems with constraints.

(Un)Bumping Cars

Explores turning bumper cars into unbumping ones through collision avoidance algorithms and the challenges faced when implementing ellipsoid barrier functions.

International Portfolio Allocation

Explores the optimization of international portfolio allocation and the principles of comparative advantage in trade.