When Prospect Theory Meets Mean-Reverting Asset Returns: A Behavioral Dynamic Trading Model

We develop a continuous-time asset allocation model to investigate the effects of mean-reverting stock returns on investors with Prospect Theory (PT) preferences. Our semi-analytical solution facilitates a comprehensive exploration of how the stock investment of PT investors may differ when accounting for mean reversion. We find that incorporating mean reversion attenuates the distinct V-shaped demand pattern in relation to contemporaneous prices, which is more pronounced when mean reversion is absent, by significantly reducing PT investors’ stock demand following price increases. This shift leads to a stock demand profile that demonstrates an inverse relationship with stock prices. In line with this change, we also show that combining PT utility with mean reversion predicts short-term contrarian behavior and the disposition effect more reliably than benchmark models that incorporate either PT utility or mean-reverting returns alone.