A Simple Algorithm for the Portfolio Selection Problem

Authors

  • ALAN L. LEWIS

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    • Analytic Investment Management, Inc., Irvine, California. The author gratefully acknowledges stimulating conversations over the years on portfolio theory with Sheen T. Kassouf.


ABSTRACT

The author presents a rapidly convergent algorithm to solve the general portfolio problem of maximizing concave utility functions subject to linear constraints. The algorithm is based on an iterative use of the Markowitz critical line method for solving quadratic programs. A simple example, taken from the theory of state-contingent claims, is worked out in detail. For technical convergence results, the reader is referred to the appropriate mathematical programming literature.

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