Dynamic Portfolio Selection and Asset Pricing under Neo-Additive Probability Weighting

We study a dynamic portfolio selection problem in which an agent trades a stock and a risk-free asset with the objective of maximizing the rank-dependent utility of her wealth at the terminal time of the investment horizon. Due to time inconsistency, we consider three types of agents, pre-committed, sophisticated, and naive agents, who differ from each other in whether they are aware of the time inconsistency and whether they have self-control. Assuming a neo-additive probability weighting function, we solve the strategies of these agents. We find that the pre-committed agent takes a loss-exit strategy, leading to a positively skewed terminal wealth, and that the sophisticated agent takes less risk at the initial time than the pre-committed and naive agents do. We also study equilibrium asset pricing and find that with pre-committed agents, the stock return exhibits a reversal effect, and the initial stock price is lower than in the case when the market is populated with sophisticated agents