Optimal allocation-consumption problem for a portfolio with an illiquid asset
Artikel i vetenskaplig tidskrift, 2016

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.

91G10

illiquidity

random income

49L25

Mathematics

portfolio optimization

49L20

viscosity solutions

35Q93

91G80

Författare

L. A. Bordag

I. P. Yamshchikov

Dmitrii Zhelezov

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

International Journal of Computer Mathematics

0020-7160 (ISSN)

Vol. 93 5 749-760

Ämneskategorier

Matematik

DOI

10.1080/00207160.2013.877584

Mer information

Skapat

2017-10-08