Dynamic portfolio selection with mispricing and model ambiguity

We investigate optimal portfolio selection problems with mispricing and model ambiguity under a financial market which contains a pair of mispriced stocks. We assume that the dynamics of the pair satisfies a “cointegrated system” advanced by Liu and Timmermann in a 2013 manuscript. The investor hopes to exploit the temporary mispricing by using a portfolio strategy under a utility function framework. Furthermore, she is ambiguity-averse and has a specific preference for model ambiguity robustness. The explicit solution for such a robust optimal strategy, and its value function, are derived. We analyze these robust strategies with mispricing in two cases: observed and unobserved mean-reverting stochastic risk premium. We show that the mispricing and model ambiguity have completely distinct impacts on the robust optimal portfolio selection, by comparing the utility losses. We also find that the ambiguity-averse investor who ignores the mispricing or the model ambiguity, suffers a substantially larger utility loss if the risk premium is unobserved, compared to when it is observed.