Optimization Methods in Finance

Course Diary

For classes that have not happen yet, the entries are approximate.

  • 01/26: course information and logistics, introduction to optimization, examples of computational finance problems, linear programming settings, duality, optimality of extreme points.
  • 02/02: basic feasible solutions, basic directions, reduced costs, step size, the simplex algorithm, the dual simplex, derivatives and options, asset pricing through replications.
  • 02/09: asset pricing, rational pricing, risk-neutral probabilities, first fundamental theorem of asset pricing, integer programming, combinatorial auctions, geometry of feasible region, branch and bound basics.
  • 02/16: branching rules, search strategies, cutting planes, Gomory mixed cuts, guest lecture by Serdar Kadioglu from Oracle.
  • 02/23: building index funds with integer programming.
  • 03/02: non-linear programming, Lagrangian, duality, Slater's condition, KKT conditions, gradient descent, Newton's method, subgradient methods.
  • 03/09: quadratic programming, geometric programming, interior point methods, logarithmic barrier, central path, barrier method.
  • 03/16: primal-dual interior point method, portfolio optimization.
  • 03/23: return-based style analysis, conic optimization.
  • 03/30: no class (spring break).
  • 04/06: stochastic optimization, L-shaped algorithm.
  • 04/13: generating scenarios, Value-at-Risk, Conditional Value-at-Risk
  • 04/20: no class
  • 04/27: robust optimization