### 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.

Original language | English |
---|---|

Article number | 127571 |

Journal | Advances in Decision Sciences |

Volume | 2012 |

DOIs | |

Publication status | Published - 2012 |

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### ASJC Scopus subject areas

- Decision Sciences(all)
- Applied Mathematics
- Computational Mathematics
- Statistics and Probability

### Cite this

*Advances in Decision Sciences*,

*2012*, [127571]. https://doi.org/10.1155/2012/127571

**Statistical portfolio estimation under the utility function depending on exogenous variables.** / Hamada, Kenta; Wei Ye, Dong; Taniguchi, Masanobu.

Research output: Contribution to journal › Article

*Advances in Decision Sciences*, vol. 2012, 127571. https://doi.org/10.1155/2012/127571

}

TY - JOUR

T1 - Statistical portfolio estimation under the utility function depending on exogenous variables

AU - Hamada, Kenta

AU - Wei Ye, Dong

AU - Taniguchi, Masanobu

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84856415750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856415750&partnerID=8YFLogxK

U2 - 10.1155/2012/127571

DO - 10.1155/2012/127571

M3 - Article

VL - 2012

JO - Advances in Decision Sciences

JF - Advances in Decision Sciences

SN - 2090-3359

M1 - 127571

ER -