Robust Merton Problem with Nondominated Priors

Abstract: 

We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time. We also incorporate the investor’s prior belief about the future distribution of the market via a penalization term. We solve the robust optimization problem explicitly both when the investor’s utility is of logarithmic type. Accounting on the prior belief results in a non-corner solution, which is different from the usual results in a robust optimization problem.