Optimal Utility with Some Additional Information

Abstract

A utility optimization problem for continuous time financial markets is examined in the presence of additional information. Three cases, including “side information known in advance,” “information disclosure at the market-known time,” and “information disclosure at the market-unknown time,” are discussed. The martingale representation theorems for each case are obtained by using stochastic filtering technique. In the case of logarithmic utility, the analytic forms of optimal solutions are obtained and the effect of these kinds of additional information to investor's strategies are revealed.

Keywords:

• Martingale method
• Stochastic filtering
• Utility optimization

Mathematics Subject Classification:

• Primary 90A09
• 60G44
• 60H05
• Secondary 60H30
• 90A35
• 90A43
• 90A11

ACKNOWLEDGEMENT

This work is supported by the National Natural Science Foundation of China under Grant No. 10171066 and Shanghai Key Project under Grant No.02DJ14063.