2016/13  LEM Working Paper Series  
Wealth and Price Distribution by Diffusive Approximation in a Repeated Prediction Market 

Giulio Bottazzi and Daniele Giachini 

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


JEL Classifications  
C60, D53, G11, G12


Abstract  
The approximate agents' wealth and price invariant densities of a
repeated prediction market model is derived using the FokkerPlanck
equation of the associated continuoustime jump process. We show
that the approximation obtained from the evolution of logwealth
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 closedform solution for the price distribution which is
asymptotically correct.
 
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