Quasi-analytical solution of an investment problem with decreasing investment cost due to technological innovations

Abstract

In this paper we address, in the context of real options, an investment problem with two sources of uncertainty: the price (reflected in the revenue of the firm) and the level of technology. The level of technology impacts in the investment cost, that decreases when there is a technology innovation. The price follows a geometric Brownian motion, whereas the technology innovations are driven by a Poisson process. As a consequence, the investment region may be attained in a continuous way (due to an increase of the price) or in a discontinuous way (due to a sudden decrease of the investment cost). For this problem no analytical solution is known, and threfore we propose a quasi-analytical method to find an approximated solution that preserves the qualitative features of the exact solution. This method is based on a truncation procedure. We prove that the truncated solution converges to the solution of the original problem. We provide results of the comparative statics for the investment thresholds. These results show interesting behaviors. In particular the investment may be postponed or anticipated with the intensity of the technology innovations and with the impact on the investment cost.