Value of flexibility in a finite horizon decision process

Motivated by a model of decision processes of R&D projects, we consider a finite horizon Markov decision process. In this context the difference between the value under active control (when the process is optimally controlled) and under passive control (when the control at each stage is a default control) is called the value of flexibility. We analyze the impact of increased variability of the terminal payoff on the value of flexibility and the optimal value of the project and show that the impact of increased variability on the passive project can be used to determine the impact of increased variability on the optimally controlled project.