Nonlinear Optimization with Financial Applications [Hardcover]

This instructive book introduces the key ideas behind practical nonlinear optimization, accompanied by computational examples and supporting software. It combines computational finance with an important class of numerical techniques.

The book introduces the key ideas behind practical nonlinear optimization. Computational finance  an increasingly popular area of mathematics degree programs  is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material  which occupies about one-third of the text  is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performance is demonstrated on a range of optimization problems arising in financial mathematics. Theoretical convergence properties of methods are stated, and formal proofs are provided in enough cases to be instructive rather than overwhelming. Practical behavior of methods is illustrated by computational examples and discussions of efficiency, accuracy and computational costs. Supporting software for the examples and exercises is available (but the text does not require the reader to use or understand these particular codes). The author has been active in optimization for over thirty years in algorithm development and application and in teaching and research supervision.

List of FiguresList of TablesPreface 1: PORTFOLIO OPTIMIZATION1. Nonlinear optimization2. Portfolio return and risk3. Optimizing two-asset portfolios4. Minimimum risk for three-asset portfolios5. Two- and three-asset minimum-risk solutions6. A derivation of the minimum risk problem7. Maximum return problems2: ONE-VARIABLE OPTIMIZATION1. Optimality conditions2. The bisection method3. The secant method4. The Newton method5. Methods using quadratic or cubló¾