Prediction Markets, Heterogeneous Beliefs, Fractional Kelly Rule, Invariant Distribution, Diffusive Approximation, Fokker Planck Equation

C60, D53, G11, G12

The approximate agents' wealth and price invariant densities of a repeated prediction market model is derived using the Fokker-Planck equation of the associated continuous-time jump process. We show that the approximation obtained from the evolution of log-wealth difference can be reliably exploited to compute all the quantities of interest in all the acceptable parameter space. When the risk aversion of the trader is high enough, we are able to derive an explicit closed-form solution for the price distribution which is asymptotically correct.