Principles of Optimization for Portfolio Selection

Valuation, Financial Modeling, and Qualitative Tools

5. Mathematical Tools and Techniques for Financial Modeling and Analysis

Optimization and Simulation Tools

  1. Stoyan V. Stoyanov Chief Financial Researcher PhD1,
  2. Svetlozar T. Rachev Chair-Professor PhD, Dr Sci2,
  3. Frank J. Fabozzi Professor PhD, CFA, CPA3

Published Online: 15 SEP 2008

DOI: 10.1002/9780470404324.hof003066

Handbook of Finance

Handbook of Finance

How to Cite

Stoyanov, S. V., Rachev, S. T. and Fabozzi, F. J. 2008. Principles of Optimization for Portfolio Selection. Handbook of Finance. III:5:66.

Author Information

  1. 1

    FinAnalytica Inc.

  2. 2

    Chair of Econometrics, Statistics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and Department of Statistics and Applied Probability University of California, Santa Barbara

  3. 3

    Practice of Finance, Yale School of Management

Publication History

  1. Published Online: 15 SEP 2008


The mathematical theory of optimization has a natural application in the field of finance. From a general perspective, the behavior of economic agents in the face of uncertainty involves balancing expected risks and expected rewards. For example, the portfolio choice problem concerns the optimal trade-off between risk and reward. A portfolio is said to be optimal in the sense that it is the best portfolio among many alternative ones. The criterion that measures the quality of a portfolio relative to the others is known as the objective function in optimization theory. The set of portfolios among which we are choosing is called the “set of feasible solutions” or the “set of feasible points.”


  • optimization;
  • optimal;
  • objective function;
  • set of feasible solutions;
  • set of feasible points;
  • constraint set;
  • saddle point;
  • linear problems;
  • quadratic problems;
  • convex problems;
  • unconstrained optimization;
  • convex functions;
  • function;
  • functional;
  • quasi-convex functions;
  • quasi-concave;
  • convex programming;
  • Langrange multipliers;
  • Lagrangian;
  • linear programming;
  • quadratic programming