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Preface. BACKGROUND. Financial Problems and Numerical Methods. NUMERICAL METHODS. Basics of Numerical Analysis. Optimization Methods. Principles of Monte Carlo Simulation. Finite Difference Methods for Partial Differential Equations. APPLICATIONS TO FINANCE. Optimization Models for Portfolio Management. Option Valuation by Monte Carlo Simulation. Option Valuation by Finite Difference Methods. APPENDICES. Appendix A: Introduction to MATLAB Programming. Appendix B: A Refresher of Probability Theory. Index.