This paper solves the optimal investment and consumption strategies for a risk-averse and ambiguity-averse agent in an incomplete financial market with model uncertainty. The market incompleteness arises from investment constraints of the agent, while the model uncertainty stems from drift and volatility processes for risky stocks in the financial market. The agent seeks her best and robust strategies via optimizing her robust forward investment and consumption preferences. Her robust forward preferences and the associated optimal strategies are represented by solutions of ordinary differential equations, when there are both drift and volatility uncertainties, and infinite horizon backward stochastic differential equations, coupled with ordinary differential equations, when there is only drift uncertainty.
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