Non-monotonic Utility Theory-based Portfolio Selection Problem

In this paper, we consider a portfolio selection problem based on a class ofnon-monotone utility functions. The approach given here is to revise the non-monotoneutility functions being monotone utility functions.The main results are as follows:First of all, we give an example with monotone mean-variance utility functions for asimple application in the financial market.Next, in the setting of the non-monotone utility function revised to be a monotoneutility function, we arrived at the extended monotone capital asset pricing models, withloosing some assumptions. These models are closer to the real marketplace.At the end, once the non-monotone utility function being revised to a monotoneutility function, we study the multi-period and continuous-time optimal investmentconsumption choice model, and give an optimal solution to the model. This result can beregarded as the generalization of the portfolio selection with monotone utility functions.