BAYESIAN INTERPRETATION OF CONTINUOUS-TIME UNIVERSAL PORTFOLIOS(Special Issue on Theory, Methodology and Applications in Financial Engneering)

Abstract

Under the continuous-time framework with incomplete information on asset price processes, we show that the universal portfolio coincides with the optimal Bayes portfolio, which have been studied intensively in the financial economics literature. That is, we can interpret the universal portfolio as simultaneously estimating the drift and controlling the portfolio. This result holds in the finite terminal-time setting of the investment horizon. Moreover, we investigate the asymptotic behavior of the universal portfolio along its original definition and obtain a result that in the long run, the universal portfolio with incomplete information converges to the optimal portfolio with complete information.