Conditioning the information in portfolio optimization

This paper proposes a theoretical analysis on the impacts of using a suboptimal information set on the three main components used in asset pricing, namely the risk physical and neutral measures and the relative pricing kernel.The analysis is carried out by means of a portfolio optimization problem for a small and rational investor. Solving for the maximal expected utility of terminal wealth, we prove the existence of an information premium between what is required by the theory, a complete information set thus a fully conditional measure, and what is instead achievable by en econometrician. Searching for the best bounds, we then study the impact of the premium on the pricing kernel. Finally, exploiting the strong interconnection between the pricing kernel and its densities, the extension to the risk-neutral measure follows naturally