FURTHER RESULTS ON ASSET PRICING WITH INCOMPLETE INFORMATION

This paper extends the analysis of asset pricing when information is incomplete by relaxing some of the restrictive assumptions of the Gaussian model studied earlier in the literature. For the information structure considered, the posterior beliefs of the investor (the conditional distribution of the current state given the past observations) are characterized by two sets of sufficient statistics implementable in the form of a filter, (i) the vector of conditional means and (ii) a set of sufficient statistics for the conditional variance-covariance matrix. A separation theorem is demonstrated and used to produce a closed-form solution for the interest rate process when the investor's utility function is logarithmic. In this context we examine the informational efficiency properties of the interest rate and analyze the stochastic shifts in the volatility of the interest rate process. © 1991.