Mean-variance portfolio selection with random investment horizon

Jingzhen Liu; Ka-Fai Cedric Yiu; Xun Li; Tak Kuen Siu; Kok Lay Teo

doi:10.3934/jimo.2022147

Mean-variance portfolio selection with random investment horizon

Jingzhen Liu, Ka-Fai Cedric Yiu^*, Xun Li, Tak Kuen Siu, Kok Lay Teo

^*Corresponding author for this work

Department of Actuarial Studies and Business Analytics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

196 Downloads (Pure)

Abstract

This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem.

Original language	English
Pages (from-to)	4726-4739
Number of pages	14
Journal	Journal of Industrial and Management Optimization
Volume	19
Issue number	7
DOIs	https://doi.org/10.3934/jimo.2022147
Publication status	Published - Jul 2023

Bibliographical note

©2022 The Author(s). Published by AIMS, LLC. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Mean variance
random time horizon
HJB equations
efficient frontier

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10.3934/jimo.2022147Licence: CC BY

Publisher version (open access)Final published version, 380 KBLicence: CC BY

Cite this

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title = "Mean-variance portfolio selection with random investment horizon",

abstract = "This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem.",

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AU - Yiu, Ka-Fai Cedric

AU - Li, Xun

AU - Siu, Tak Kuen

AU - Teo, Kok Lay

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N2 - This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem.

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KW - Mean variance

KW - random time horizon

KW - HJB equations

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JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

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Mean-variance portfolio selection with random investment horizon

Abstract

Bibliographical note

Keywords

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