The Optimal Portfolio Selection Model under g -Expectation

Abstract

This paper solves the optimal portfolio selection model under the framework of the prospect theory proposed by Kahneman and Tversky in the 1970s with decision rule replaced by the $g$-expectation introduced by Peng. This model was established in the general continuous time setting and firstly adopted the $g$-expectation to replace Choquet expectation adopted in the work of Jin and Zhou, 2008. Using different S-shaped utility functions and $g$-functions to represent the investors' different uncertainty attitudes towards losses and gains makes the model not only more realistic but also more difficult to deal with. Although the models are mathematically complicated and sophisticated, the optimal solution turns out to be surprisingly simple, the payoff of a portfolio of two binary claims. Also I give the economic meaning of my model and the comparison with that one in the work of Jin and Zhou, 2008.