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.

在本文中，我们在实物期权的背景下解决了具有两个不确定性来源的投资问题：价格（反映在公司的收入中）和技术水平。技术水平影响投资成本，当有技术创新时，投资成本会降低。价格遵循几何布朗运动，而技术创新则由泊松过程驱动。因此，投资区域可能以连续方式（由于价格上涨）或以不连续方式（由于投资成本突然下降）获得。对于这个问题没有已知的解析解，因此我们提出了一种准解析方法来找到一个近似解，保留精确解的定性特征。该方法基于截断过程。我们证明截断的解收敛到原始问题的解。我们提供了投资门槛的比较静态结果。这些结果显示了有趣的行为。特别是随着技术创新的强度和对投资成本的影响，投资可能会被推迟或预期。