Practical Financial Optimization: Decision Making for Financial Engineers

Foreword

This volume is both a comprehensive guide to optimization techniques useful in financial decision making and a well-illustrated essay on the relationship between theory and practice. Often in practice the real problem, in complete detail, is beyond optimization. It involves more possible hypotheses about the world we face, and more degrees of freedom in the part of the world we control, than we have time to specify. The practical user of optimization techniques must write down in an explicit formal model a “small world,” as Savage called it, which, on the one hand, can be solved by available techniques and, on the other hand, captures the essence of the real problem. The small world of the formal model may seem large, involving many thousands of variables and constraints, but may be dwarfed by the astronomical size of the real problem. Rigorous mathematical arguments can demonstrate that particular computational procedures will solve certain classes of problems. In contrast, there is no such demonstrable procedure for how to formulate the formal model so as to capture the essence of the real problem.

I often use simulation analysis to help decide the details of an optimization analysis to be deployed in a practical setting. For example, a client of mine runs a group of funds, the oldest of which has outperformed its benchmark eight of nine years since inception, as well as substantially outperforming on average. (The funds exploit special properties of a certain class ...