Incorporating views on marginal distributions in the calibration of risk models

We apply entropy based ideas to portfolio optimization and options pricing. The known abstracted problem corresponds to finding a probability measure that minimizes relative entropy with respect to a specified measure while satisfying moment constraints on functions of underlying assets. We generalize this to also allow constraints on marginal distribution of functions of underlying assets. These are applied to Markowitz portfolio framework to incorporate fatter tails as well as to options pricing to incorporate implied risk neutral densities on liquid assets.