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

31 Pages Posted: 7 Aug 2007 Last revised: 11 May 2010

See all articles by Zhaojun Yang

Zhaojun Yang

Southern University of Science and Technology - Department of Finance

Christian-Oliver Ewald

University of Glasgow; Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance

Wen-Kai Wang

National University of Kaohsiung - Department of Finance

Date Written: August 1, 2007

Abstract

In this paper 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 semi-analytical formula, which uses as an input the numerical solution of a system of ODE's. For both cases we present a comparative analysis.

Keywords: Partial information, value of information, stochastic optimal control, stochastic filtering, information economics

JEL Classification: D82, C61, G11, D81

Suggested Citation

Yang, Zhaojun and Ewald, Christian-Oliver and Wang, Wen-Kai, A Comparative Analysis of the Value of Information in a Continuous Time Market Model with Partial Information: The Cases of Log-Utility and CRRA. (August 1, 2007). Available at SSRN: https://ssrn.com/abstract=1005106 or http://dx.doi.org/10.2139/ssrn.1005106

Zhaojun Yang

Southern University of Science and Technology - Department of Finance ( email )

No 1088, Xueyuan Rd.
District of Nanshan
Shenzhen, Guangdong 518055
China

HOME PAGE: http://fin.sustc.edu.cn/Case-detail-id-21.html

Christian-Oliver Ewald (Contact Author)

University of Glasgow ( email )

Adam Smith Building
Glasgow, Scotland G12 8RT
United Kingdom

Center for Dynamic Macroeconomic Analysis, University of St. Andrews - School of Economics and Finance ( email )

Castlecliffe
The Scores
St. Andrews, Fife KY16 9AL
United Kingdom
+44(0)1334 462435 (Phone)

HOME PAGE: http://www.maths.usyd.edu.au/u/ewald/

Wen-Kai Wang

National University of Kaohsiung - Department of Finance ( email )

700 Kaohsiung University Rd.
Nanzih District
Kaohsiung 803
Taiwan

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