Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

Real option model of dynamic growth processes with consumption

Pages: 2223 – 2239



Nengsheng Fang (School of Finance, Southwestern University of Finance and Economics, Chengdu, China; and Collaborative Innovation Center of Financial Security, China)

Xinfeng Ruan (School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, China)

Caixiu Liao (School of Mathematical Sciences, South China Normal University, Guangzhou, China)


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.


real option, asset pricing, jump diffusion, optimal consumption strategy, risk premium

2010 Mathematics Subject Classification

35Q91, 60G20

Published 3 September 2015