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Title of Journal: J Optim Theory Appl

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Abbravation: Journal of Optimization Theory and Applications

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Springer US

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DOI

10.1016/1040-6190(94)90292-5

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1573-2878

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An Algorithm for Portfolio Optimization with Varia

Authors: M J Best J Hlouskova
Publish Date: 2007/07/20
Volume: 135, Issue: 3, Pages: 563-581
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Abstract

A portfolio optimization problem consists of maximizing an expected utility function of n assets At the end of a typical time period the portfolio will be modified by buying and selling assets in response to changing conditions Associated with this buying and selling are variable transaction costs that depend on the size of the transaction A straightforward way of incorporating these costs can be interpreted as the reduction of portfolios’ expected returns by transaction costs if the utility function is the meanvariance or the power utility function This results in a substantially higherdimensional problem than the original ndimensional one namely 2K+1ndimensional optimization problem with 4K+1n additional constraints where 2K is the number of different transaction costs functions The higherdimensional problem is computationally expensive to solve This twopart paper presents a method for solving the 2K+1ndimensional problem by solving a sequence of ndimensional optimization problems which account for the transaction costs implicitly rather than explicitly The key idea of the new method in Part 1 is to formulate the optimality conditions for the higherdimensional problem and enforce them by solving a sequence of lowerdimensional problems under the nondegeneracy assumption In Part 2 we propose a degeneracy resolving rule address the efficiency of the new method and present the computational results comparing our method with the interiorpoint optimizer of MosekThis research was supported by the National Science and Engineering Research Council of Canada and the Austrian National Bank The authors acknowledge the valuable assistance of Rob Grauer and Associate Editor Franco Giannessi for thoughtful comments and suggestions

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