Aggregation oh Heterogeneous Beliefs, Asset Pricing and Risk Sharing in Complete Financial Markets

We propose a method to aggregate heterogeneous individual beliefs, givena competitive equilibrium in complete asset markets, into a single "marketprobability" such that it generates, if commonly shared by all investors, thesame marginal valuation of assets by the market (the same equilibrium prices)as well as by each individual investor. As a result of the aggregation process,the market portfolio may have to be scalarly adjusted, upward or downward,a re‡ection of an "aggregation bias" due to the diversity of beliefs.From a "dual" viewpoint, the standard construction of an "expected utilitymaximizing aggregate investor" designed to "represent" the economy inequilibrium, is shown to be also valid in the case of heterogeneous beliefs,modulo the above scalar adjustment of the market portfolio, thereby generatingan "Adjusted" version of the "Consumption based Capital Asset PricingModel" (ACCAPM). The allocation of aggregate and individual risks (mutualization)is then analyzed in relation to deviations of individual beliefsfrom the aggregate "market probability". Finally, we identify the channelsthrough which the distributions, among investors, of individual beliefs and ofother microeconomic characteristics (incomes, attitudes toward risk), do affectpricing of risky assets and thus may, or may not, contribute to explainingsuch challenges as the so-called "equity premium puzzle".