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Advances in Decision Sciences
Volume 2012 (2012), Article ID 127571, 15 pages
http://dx.doi.org/10.1155/2012/127571
Research Article

Statistical Portfolio Estimation under the Utility Function Depending on Exogenous Variables

Department of Applied Mathematics, School of Fundamental Science and Engineering, Waseda University, Tokyo 169-8050, Japan

Received 8 September 2011; Accepted 15 November 2011

Academic Editor: Cathy W. S. Chen

Copyright © 2012 Kenta Hamada et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In the estimation of portfolios, it is natural to assume that the utility function depends on exogenous variable. From this point of view, in this paper, we develop the estimation under the utility function depending on exogenous variable. To estimate the optimal portfolio, we introduce a function of moments of the return process and cumulant between the return processes and exogenous variable, where the function means a generalized version of portfolio weight function. First, assuming that exogenous variable is a random process, we derive the asymptotic distribution of the sample version of portfolio weight function. Then, an influence of exogenous variable on the return process is illuminated when exogenous variable has a shot noise in the frequency domain. Second, assuming that exogenous variable is nonstochastic, we derive the asymptotic distribution of the sample version of portfolio weight function. Then, an influence of exogenous variable on the return process is illuminated when exogenous variable has a harmonic trend. We also evaluate the influence of exogenous variable on the return process numerically.