Optimal Portfolio of Low Liquid Assets with a Power Utility Function

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 4, Page 687--726.

Matsumoto, Koichi
Optimal Portfolio of Low Liquid Assets with a Power Utility Function
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]


Abstract:
When an asset is completely liquid, an investor can realize his desirable strategy. But when the asset is not sufficiently liquid, the investor cannot trade the asset continuously and his strategy is restricted. He has to consider the risk of the failure of the trade. In this paper a risky asset is traded at the random times and an investor has a power utility function. In this situation we solve an optimal portfolio problem. We propose an asymptotic expansion of the optimal strategy. Further we discuss convergence of the value function when the asset becomes liquid.

Keywords: Portfolio optimization, liquidity, power utility function

Mathematics Subject Classification (2000): Primary 91B28; Secondary 93E20
Mathematical Reviews Number: MR2037764

Received: 2002-12-03