Transcription of Optimization Methods in Finance - ku
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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.)
10 CHAPTER 1. INTRODUCTION unbounded, then it is often possible to nd a solution x 2 S that satis es f(x ) f(x); 8x 2 S: Such an x is called a global minimizer of the problem (1.1). If f(x ) < f(x); 8x 2 S; x 6= x ; then x is a strict global minimizer. In other instances, we may only nd an x 2 S that satis es f(x ) f(x); 8x 2 S \ Bx (")
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