Robust portfolio choice with limited attention

This paper investigates a robust portfolio selection problem with the agent's limited attention. The agent has access to a risk-free asset and a stock in a financial market. But she does not observe perfectly the expected return rate of the stock so she has to estimate this key parameter before making decisions. Besides the general observable financial information, the agent can also acquire a news signal process whose accuracy depends on the agent's attention. We assume that the agent pays limited attention on the signal and she does not trust her estimation model. So it is necessary to consider model ambiguity in this paper as well. The agent maximizes the expected utility of her terminal wealth under the worst-case scenario. Under this setting, we derive the robust optimal strategy explicitly. In the presence of the attention and ambiguity aversion, the myopic term of the strategy, the hedging term of the strategy and the worst-case scenario are all changed. We find that more attention makes the variance of the estimated return smaller. The numerical examples also show that a more attentive agent has a better estimation of the unobservable parameter and is more confident on her estimation. Consequently, the worst-case scenario deviates less from the reference model, which implies a higher expected return rate under the worst-case scenario, thus invests more in the stock.