Conditional investment policy under uncertainty and irreversibility
An irreversible investment decision, such as fixing a defective equipment is considered, which in turn is conditional on the profitability and expected life of the entire equipment. Given the sunk cost of fixing the fault, the uncertain costs of waiting and the expected life of the entire equipment, the problem is to find the optimal time to fix the fault to minimize the expected total discounted costs. The optimal policy is obtained in the optimal stopping context using stochastic dynamic programming techniques, and analyzed via the partial differential equation (PDE). It is shown that increasing uncertainty over internal losses (as a function of profits) and decreasing life expectancy of the entire equipment can significantly increase the optimal stopping barrier.
investment irreversibility optimal stopping stochastic processes