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

L. A. Bordag ; I. P. Yamshchikov ; Dmitrii Zhelezov (Institutionen för matematiska vetenskaper)
International Journal of Computer Mathematics (0020-7160). Vol. 93 (2016), 5, p. 749-760.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: 91G10, 35Q93, 49L25, 91G80, 49L20, portfolio optimization, random income, viscosity solutions, illiquidity, Mathematics



Denna post skapades 2016-05-06. Senast ändrad 2016-06-02.
CPL Pubid: 236040

 

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