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.
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