2021/03/15 by Dammann, Felix, Ferrari, Giorgio
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2103.08258
We consider a real options model for the optimal irreversible investment problem of a profit maximizing company. The company has the opportunity to invest into a production plant capable of producing two products, of which the prices follow two independent geometric Brownian motions. After paying a constant sunk investment cost, the company sells the products on the market and thus receives a continuous stochastic revenue-flow. This investment problem is set as a two-dimensional optimal stopping problem. We find that the optimal investment decision is triggered by a convex curve, which we characterize as the unique continuous solution to a nonlinear integral equation. Furthermore, we provide analytical and numerical comparative statics results of the dependency of the project's value and investment decision with respect to the model's parameters.