Title: Principles of Bayesian portfolio choice
Authors: Jan Vecer - Charles University, MFF, Ke Karlovu 3, 121 16 Praha 2 (Czech Republic) [presenting]
Abstract: Utility maximization depends on the choice of the underlying riskless asset as a numeraire. We show that the only numeraire invariant utility is a logarithmic function. We also note that the prices can be expressed as the likelihood ratio of the respective state price densities. On the other side, each state price density generates an asset that corresponds to the log utility optimal portfolio with respect to all assets. This is important in portfolio diversification; more opinions about the state price density generate more assets to invest in. We show that the expected log return of the price is a relative entropy between the state price densities. When the market agent that maximizes log utility uses a mixture distribution of the state price densities of the market assets, the resulting optimal portfolio is static. When the market agent uses a prior distribution for her market opinion distribution, the resulting wealth of each parameter updates in a Bayesian fashion.