Robust Portfolio Selection with Generalized Preferences : A Methodology for Private Banking

This paper is a first attempt to develop a methodology, consistent with non-linear probability weighting, to construct portfolios for Private Banking customers. Empirical evidence suggests that decision makers transform probability kernels in a non-linear way (Kahneman and Tversky (1992), Prelec (1998)). This has led to the concept of probability weighting function. Standard finance theory, and notably portfolio theory, has not yet dealt with such behavior. Part of the reason is that such behavior is considered non rational. It is first shown how to estimate the preferences from individual customers' data. The paper, then shows that probability weighting may be very rational. Indeed, it may be derived from the maximization of a measure of uncertainty (entropy) given observed data. It is then shown how a dynamic continuous time portfolio choice problem can be easily solved. It is assumed that probability weighting stems from robust behavior in face of parametric uncertainty. With this interpretation, risk behavior determines the functional form of the utility function, whereas probability weighting stems from an information treatment recipe. In fact, our decision maker chooses parameters that maximize a maximum entropy likelihood function. The decision maker internalizes the fact that the observed likelihood is one of many possible. Finally, the subjectively robust parameters can then be used to derive the optimal policy rule of a dynamic continuous time portfolio model