Journal of Probability and Statistics
Volume 2011 (2011), Article ID 238623, 23 pages
doi:10.1155/2011/238623
Research Article

A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA

1School of Finance and Statistics, Hunan University, Changsha 410079, China
2School of Mathematics and Statistics, University of Sydney, Sydney NSW 2006, Australia

Received 16 March 2010; Accepted 12 May 2010

Academic Editor: Tak Kuen Siu

Copyright © 2011 Zhaojun Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the question what value an agent in a generalized Black-Scholes model with partial information attributes to the complementary information. To do this, we study the utility maximization problems from terminal wealth for the two cases partial information and full information. We assume that the drift term of the risky asset is a dynamic process of general linear type and that the two levels of observation correspond to whether this drift term is observable or not. Applying methods from stochastic filtering theory we derive an analytical tractable formula for the value of information in the case of logarithmic utility. For the case of constant relative risk aversion (CRRA) we derive a semianalytical formula, which uses as an input the numerical solution of a system of ODEs. For both cases we present a comparative analysis.