Real option model of dynamic growth processes with consumption

A real option model is built upon a set of stochastic processes for some real investment decision making in incomplete markets. Typically, the optimal consumption level is obtained under a logarithmic utility constraint, and a partial integro-differential equation (PIDE) of the real option is deduced by martingale methods. Analytical formulation of the PIDE is solved by Fourier transformation. Two types of decision making strategies, i.e. option price and IRP (inner risk primium) comparisons, are provided. Finally, the Monte Carlo simulation and numerical computation are illustrated to verify the conclusions.