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Optimization Methods in Finance - ku

Optimization Methods in Finance Gerard Cornuejols tu Reha Tu ncu . Carnegie Mellon University, Pittsburgh, PA 15213 USA. January 2006. 2. Foreword Optimization models play an increasingly important role in financial de- cisions. Many computational Finance problems ranging from asset allocation to risk management, from option pricing to model calibration can be solved efficiently using modern Optimization techniques. This course discusses sev- eral classes of Optimization problems (including linear, quadratic, integer, dynamic, stochastic, conic, and robust programming) encountered in finan- cial models. For each problem class, after introducing the relevant theory (optimality conditions, duality, etc.) and efficient solution Methods , we dis- cuss several problems of mathematical Finance that can be modeled within this problem class. In addition to classical and well-known models such as Markowitz' mean-variance Optimization model we present some newer Optimization models for a variety of financial problems.

20.1 Robust Multi-Period Portfolio Selection . . . . . . . . . . . . 309 ... to a single-objective optimization problem or a sequence of such problems. If the decision variables in an optimization problem are restricted to integers, or to a discrete set of possibilities, we have an integer or discrete ...

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