The Optimal Portfolio Selection Model Under Prospect Theory And G-expectation

This paper solves the optimal portfolio selection model under the frame-work of the prospect theory proposed by Kahneman and Tversky in 1970s and the g-expectation by peng. This model was established in the general continuous time setting and firstly adopted the g-expectation to replace the nonlinear expectation, for example the choquet expectation in [1]. Using different S-shaped utility functions to represent the investors'different at-titudes towards losses and gains, distorting the objectively probability in the form of g-expectation, these not only make the model more realistic but also more difficult to deal with. We deduce the wealth equation in complete market from linear in [1] to super-linear case which will incorporate more realistic cases, for example the risk premium different for the short and long positions. 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 options. Also we find that our optimal solution has the similar form with the one in [1] when all the g functions are the same linear case, but they are different in essence. At last, we solve out an concrete example with CRRA utility function finding out the opti-mal investment strategy and find the economic meaning behind the symbols which greatly enhance the application of our model.