Abstract
This paper considers multiple market agents who have distinct distributional opinions about the state price density. Different opinions can be contested on a hypothetical market that trades Arrow-Debreu securities. We focus on the situation when the agents are maximizing logarithmic utility as this generalizes the Kelly criterion to multiple and infinite number of outcomes. We determine analytically the optimal volumes for the Arrow-Debreu securities to be traded and show that the agent's increase of the expected utility corresponds to the relative entropy between her and the market distributions also known as a Kullback-Leibler divergence. The distributional opinions reach an equilibrium in the form of the linear mixture of the distributions. We show that when the the result of the outcome is observed, the profit and loss from trading updates agents' bankrolls in a Bayesian fashion. We extend these results to exponential and power utility functions.
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