This research focuses on a case where an agent makes an investment decision under rational inattention with bounded rationality. When facing multiple investment options under uncertainty, the additional information can be acquired at some cost. Real options model is applied to analyze the investment options among the multiple choices and the information cost is valued based on the Shannon's entropy. The derived multinomial logit is linked to Gibbs--Boltzmann distribution in order to prove the existence of bifurcations that give rise to a cascade of chaos. The result provides a realistic insight on the possible chaos in decision-making when facing multiple choices under limited information.

This paper formulates a capital investment problem under ambiguity as a robust control problem. We consider the problem as a particular form of the maxmin expected utility model, such that the firm's optimal decision becomes the solution of a convex-concave function. As the presence of the convex cost function with ambiguity prevents us from deriving an analytical solution, we propose a numerical procedure to derive the optimal solution via approximate dynamic programming. Sensitivity analyses are conducted to examine the impact of the acceptable degree of model misspecification, robust parameter, and volatility on firm's optimal decision-making. This paper has shown that the optimal distortion is within the acceptable degree because there is a penalty for model misspecification under an appropriate degree of acceptance. As the robust parameter increases, the magnitude of distortion decreases, creating a trade-off between the degree of acceptable misspecification and the misspecification penalty. As a result, the optimal distortion level between the reference model and the approximate model is determined. It has also shown that price risk reduces the size of the optimal distortion and the optimal investment rate. We especially note that an increase in price risk under ambiguity has the opposite impact on the optimal investment rate compared to the case under risk. The result indicates that output price ambiguity makes firms more cautious about capital investment.