Continuous Trading Dynamically Effectively Complete Market with Heterogeneous Beliefs
In a framework of heterogeneous beliefs, I investigate a two-date consumption model with continuous trading over the interval [0; T], in which information on the aggregate consumption at time T is revealed by an Ornstein-Uhlenbeck Bridge. This information structure allows investors to speculate on the heterogeneous posterior variance of dividend throughout [0; T). The market populated with many time-additive exponential-utility investors is dynamically effectively complete, if investors are allowed to trade in only two long-lived securities continuously. The underlying mechanism is that these assumptions imply that the Pareto efficient individual consumption plans are measurable with respect to the aggregate consumption. Hence, I may not need a dynamically complete market to facilitate a Pareto efficient allocation of consumption, the securities only have to facilitate an allocation which is measurable with respect to the aggregate consumption. With normally distributed dividend, the equilibrium stock price is endogenized in a Radner equilibrium as a precision weighted average of the investors? posterior mean minus a risk premium determined by the average posterior precision. The stock price is also a sufficient statistic for computation of the price of redundant dividend derivative and the equilibrium portfolios. The investors form their Pareto optimal trading strategies as if they intend to dynamically endogenously replicate the value of the dividend derivative.
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