The effect of increased risk on the expected proceeds and sale strategy of a machine

In this paper, a machine is considered that at any moment of time can be in one of a finite number of states. Transitions of the machine between states are governed by a stationary Markov chain. The sale value of the machine is a random variable depending on the state of the machine and on its age. In this case the optimal sale strategy is to sell the machine when its sale value exceeds some critical limit (which is a function of the state and age of the machine). It is shown that when uncertainty rises (or equivalently, when the dispersion of the sale value rises), the critical limits which determine the optimal sale policy also rise. It is also shown that the expected discounted proceeds from operating the machine rise when uncertainty increases. In the formulation, the sale date of the machine is a random variable which depends on the random sale value of the machine. Increased uncertainty can either increase or decrease the expected value of the sale date depending on the values of the parameters of the problem.