Optimal Consumption and Portfolio with Consistent Performance under Knight Uncertainty

The paper investigates the optimal consumption and portfolio with consistence performance under Knightian uncertainty. The agent has Knightian uncertainty for the expected return of risky asset, which is characterized by \kappa-ignorance model. Consistent performance model asks for a dynamic wealth constraint, which requires the wealth always stays at or above the weighted average of the entire historical wealth levels. In the infinite time horizon, we obtain the optimal consumption and portfolio explicit solution for the model by the HJB equation and verification theorem.