A Unified Theory: Prospect Theory and Market Dynamics

Abstract

We measure crowd’s decision weights in trading by cumulative trading volume distribution and determine a reference price about crowd’s assessment value of an individual stock by the maximal volume price in stock market. We assume that prospect theory traders derive behavioral utility in trading not only from the liquidity utility expressed in terms of final trading wealth but also from a trading weight utility and a gain-loss utility relative to the reference price. We find a mathematical relation between them, derive a price-volume differential equation, and obtain two sets of explicit trading volume distribution models. One is the models in crowd’s independent trading, and the other is the behavioral models of reference-dependent preferences in crowd’s interactive trading. Finally, we propose an explicit S-shaped value function in prospect theory from the models in crowd’s interactive trading. The unified theory is successful, consistent with empirical tests in high frequency data.