On the Amin Method and Its Applications in the Real Options with Interventions under Jump-Diffusion Processes

The paper gives proofs for the monotonicity and convexity of the Amin method to value American option under jump-diffusion processes. We also find that the Amin method is monotone for the free boundary. These properties make the Amin method appropriate for analysis in the real options with intervention, which may be biased for other numerical methods because of lack of monotonicity and convexity. The corresponding numerical results show that the market power is important for the investor in making the decision of intervention.