Robust irreversible investment strategy with ambiguity to jump and diffusion risk

Abstract This paper constructs a robust and irreversible investment rule applicable to a series of adjacent models. The project value follows a jump‐diffusion process and the investor exhibits complete ambiguity aversion or partial ambiguity aversion to the diffusion, jump amplitude, and jump frequency components. The impact of ambiguity aversion with respect to different components on the optimal investment strategy is examined. The investment decision is mainly driven by ambiguity aversion to the jump amplitude rather than frequency, and an increase in jump intensity leads to the greater importance of ambiguity aversion to jumps. We further show that ambiguity aversion regarding jumps plays a dominant role in determining the investment boundary for low volatility values, and the influence of ambiguity aversion to the diffusion part gradually outweighs that of ambiguity aversion to jumps as volatility grows.