OPTIMIZATION METHODS IN FINANCE

Transcription

1 OPTIMIZATION METHODS IN FINANCE GERARD CORNUEJOLS Carnegie Mellon University REHA TUTUNCU Goldman Sachs Asset Management CAMBRIDGE UNIVERSITY PRESS

2 Foreword page xi Introduction Optimization problems Optimization with data uncertainty Financial mathematics 8 Linear programming: theory and algorithms The linear programming problem Duality Optimality conditions The simplex method 23 LP models: asset/liability cash-flow matching Short-term financing Dedication Sensitivity analysis for linear programming Case study: constructing a dedicated portfolio 60 LP models: asset pricing and arbitrage Derivative securities and the fundamental theorem of asset pricing Arbitrage detection using linear programming Additional exercises Case study: tax clientele effects in bond portfolio management 76 Nonlinear programming: theory and algorithms Introduction Software Univariate optimization Unconstrained optimization Constrained optimization Nonsmooth optimization: subgradient methods 110 vn

3 viii 6 NLP models: volatility estimation Volatility estimation with GARCH models Estimating a volatility surface Quadratic programming: theory and algorithms The quadratic programming problem Optimality conditions Interior-point methods QP software Additional exercises QP models: portfolio optimization Mean-variance optimization Maximizing the Sharpe ratio Returns-based style analysis Recovering risk-neutral probabilities from options prices Additional exercises Case study: constructing an efficient portfolio Conic optimization tools Introduction Second-order cone programming Semidefinite programming Algorithms and software Conic optimization models in finance Tracking error and volatility constraints Approximating covariance matrices Recovering risk-neutral probabilities from options prices Arbitrage bounds for forward start options Integer programming: theory and algorithms Introduction Modeling logical conditions Solving mixed integer linear programs Integer programming models: constructing an index fund Combinatorial auctions The lockbox problem Constructing an index fund Portfolio optimization with minimum transaction levels Additional exercises Case study: constructing an index fund 224

4 ix 13 Dynamic programming methods Introduction Abstraction of the dynamic programming approach The knapsack problem Stochastic dynamic programming DP models: option pricing A model for American options Binomial lattice DP models: structuring asset-backed securities Data Enumerating possible tranches A dynamic programming approach Case study: structuring CMOs Stochastic programming: theory and algorithms Introduction Two-stage problems with recourse Multi-stage problems Decomposition Scenario generation Stochastic programming models: Value-at-Risk and Conditional Value-at-Risk Risk measures Minimizing CVaR Example: bond portfolio optimization Stochastic programming models: asset/liability management Asset/liability management Synthetic options Case study: option pricing with transaction costs Robust optimization: theory and tools Introduction to robust optimization Uncertainty sets Different flavors of robustness ' Tools and strategies for robust optimization Robust optimization models in finance Robust multi-period portfolio selection Robust profit opportunities in risky portfolios Robust portfolio selection Relative robustness in portfolio selection Moment bounds for option prices Additional exercises 318

5 A B C D References Index Convexity Cones A probability primer The revised simplex method