A1994
Title: Portfolio optimization without utility maximization with links to the frequentist and the bayesian statistics
Authors: Jan Vecer - Charles University (Czech Republic) [presenting]
Abstract: A novel approach to portfolio optimization is presented that completely bypasses utility maximization. The idea is based on a very well-known fact from option pricing that prices are likelihood ratios of the two-state price densities of the asset and the reference asset. Using this fact, one trivially concludes that the price of the optimal portfolio is simply a likelihood ratio of the physical measure used by the agent and the risk-neutral density. Furthermore, a well-known property of the likelihood ratio is that the expected log-likelihood is the relative entropy. As a consequence, it means that the expected log-returns of the portfolios are maximized for the solution in the form of the likelihood ratio. In other words, the prices are log utility optimal, but this is a consequence rather than the design. A general utility maximization can be viewed as a method to alter the physical measure to a measure closer to the risk-neutral measure in the relative entropy sense.
