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Mathematical Problems in Engineering
Volume 2016, Article ID 2813707, 12 pages
http://dx.doi.org/10.1155/2016/2813707
Research Article

Recursive Utility Maximization for Terminal Wealth under Partial Information

1Zhongtai Securities Institute for Financial Studies, Shandong University, Jinan 250100, China
2Institute of Mathematics, Shandong University, Jinan 250100, China

Received 26 October 2016; Accepted 16 November 2016

Academic Editor: Weihai Zhang

Copyright © 2016 Shaolin Ji and Xiaomin Shi. 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

This paper concerns the recursive utility maximization problem for terminal wealth under partial information. We first transform our problem under partial information into the one under full information. When the generator of the recursive utility is concave, we adopt the variational formulation of the recursive utility which leads to a stochastic game problem and characterization of the saddle point of the game is obtained. Then, we study the -ignorance case and explicit saddle points of several examples are obtained. At last, when the generator of the recursive utility is smooth, we employ the terminal perturbation method to characterize the optimal terminal wealth.