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Associate Editor Franco Giannessi for thoughtful comments and suggestions. (2007)
BibTeX
@MISC{Best07associateeditor,
author = {M. J. Best and J. Hlouskova and M. J. Best and J. Hlouskova},
title = {Associate Editor Franco Giannessi for thoughtful comments and suggestions.},
year = {2007}
}
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Abstract
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 mean-variance or the power utility function. This results in a substantially higher-dimensional problem than the original n-dimensional one, namely (2K + 1)ndimensional optimization problem with (4K + 1)n additional constraints, where 2K is the number of different transaction costs functions. The higher-dimensional problem is computationally expensive to solve. This two-part paper presents a method for solving the (2K + 1)n-dimensional problem by solving a sequence of n-dimensional 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 higher-dimensional problem and enforce them by solving a sequence
Keyphrases
thoughtful comment associate editor franco giannessi higher-dimensional problem utility function ndimensional optimization problem portfolio optimization problem n-dimensional problem n-dimensional optimization problem new method additional constraint key idea transaction cost different transaction cost function straightforward way two-part paper variable transaction cost power utility function expected utility function typical time period optimality condition
