CFRM 555 Optimization Methods in Finance

This course provides an introduction to numerical optimization methods in finance. The course will discuss the theory and efficient solution methods for major classes of optimization problems. Theoretical concepts will be paired with example applications and computing exercises. Homework problems will include use of an industrial strength optimizer to solve finance applications. Topics include:

  • Linear Programming Theory, Algorithms and Applications: feasible sets, duality, optimality conditions, simplex method, interior point methods, sensitivity analysis, asset/liability cash flow matching
  • Quadratic Programming Theory, Algorithms and Applications: constrained and unconstrained programming, optimality conditions, solution methodologies, mean-variance optimization, relationships to statistical regression, Black-Litterman, returns-based style analysis, risk-neutral density estimation
  • General Non-Linear Programming Theory, Algorithms and Applications: univariate and multivariate models, convexity, non-smooth optimization, GARCH model fitting, volatility surface estimation
  • Integer Programming Theory, Algorithms and Applications: cutting plane methods, index replication
  • Combinatorial and Network Programming Theory, Algorithms and Applications: shortest path, min-cost flow, foreign exchange, arbitrage checking
  • Cone Programming Theory, Algorithms and Applications: second-order cone programming, tracking error and volatility constraints, estimating covariance matrices
  • Dynamic Programming Theory, Algorithms and Applications: Bellman equations, forward and backward recursion, knapsack problem, option pricing, structured products
  • Stochastic Programming Theory, Algorithms and Applications: data uncertainty, multi-stage models, recourse, value at risk, conditional value at risk, asset/liability management, CVaR, transaction costs
  • Robust Optimization Theory, Algorithms and Applications: parameter uncertainty, robust constraints, robust objectives, single-period and multi-period portfolio selection
  • Additional Topics: Decomposition and Column Generation, Genetic Algorithms, Non-gradient me
Instructor: 
Steven Murray
Textbooks: 
Cornuejols and Tutuncu (2007). Optimization Methods in Finance, Cambridge University Press.
Software: 
R, open source optimizers. Other commercial portfolio optimization products such as CPLEX and Axioma, arrangements with vendors permitting.
Prerequisites: 
CFRM 542 or equivalent, or by permission. CFRM 543 Portfolio Optimization and Asset Management is desirable.
Credits: 
4