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**Harvard**

Bordag, L., Yamshchikov, I. och Zhelezov, D. (2016) *Optimal allocation-consumption problem for a portfolio with an illiquid asset*.

** BibTeX **

@article{

Bordag2016,

author={Bordag, L. A. and Yamshchikov, I. P. and Zhelezov, Dmitrii},

title={Optimal allocation-consumption problem for a portfolio with an illiquid asset},

journal={International Journal of Computer Mathematics},

issn={0020-7160},

volume={93},

issue={5},

pages={749-760},

abstract={During financial crises investors manage portfolios with low liquidity, where the paper-value of an asset differs from the price proposed by the buyer. We consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. We work in the Merton's optimal consumption framework with continuous time. The liquid part of the investment is described by a standard Black-Scholes market. The illiquid asset is sold at a random moment with prescribed distribution and generates additional liquid wealth dependent on its paper-value. The investor has a hyperbolic absolute risk aversion also denoted as HARA-type utility function, in particular, the logarithmic utility function as a limit case. We study two different distributions of the liquidation time of the illiquid asset - a classical exponential distribution and a more practically relevant Weibull distribution. Under certain conditions we show the smoothness of the viscosity solution and obtain closed formulae relevant for numerics.},

year={2016},

keywords={91G10, 35Q93, 49L25, 91G80, 49L20, portfolio optimization, random income, viscosity solutions, illiquidity, Mathematics },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 236040

A1 Bordag, L. A.

A1 Yamshchikov, I. P.

A1 Zhelezov, Dmitrii

T1 Optimal allocation-consumption problem for a portfolio with an illiquid asset

YR 2016

JF International Journal of Computer Mathematics

SN 0020-7160

VO 93

IS 5

SP 749

OP 760

AB During financial crises investors manage portfolios with low liquidity, where the paper-value of an asset differs from the price proposed by the buyer. We consider an optimization problem for a portfolio with an illiquid, a risky and a risk-free asset. We work in the Merton's optimal consumption framework with continuous time. The liquid part of the investment is described by a standard Black-Scholes market. The illiquid asset is sold at a random moment with prescribed distribution and generates additional liquid wealth dependent on its paper-value. The investor has a hyperbolic absolute risk aversion also denoted as HARA-type utility function, in particular, the logarithmic utility function as a limit case. We study two different distributions of the liquidation time of the illiquid asset - a classical exponential distribution and a more practically relevant Weibull distribution. Under certain conditions we show the smoothness of the viscosity solution and obtain closed formulae relevant for numerics.

LA eng

DO 10.1080/00207160.2013.877584

LK http://dx.doi.org/10.1080/00207160.2013.877584

OL 30