Breakthroughs and backlashes have marked progress in the development and diffusion of Artificial Intelligence (AI). These shocks make the investment in developing an Artificial General Intelligence (AGI) subject to considerable uncertainty. This paper applies a real options model, extended to account for stochastic jumps, to model the consequences of these breakthroughs and backlashes characterising on investment for an AGI. The model analytics indicate that the average magnitude and frequency of stochastic jumps will determine the optimum amount of time and money to invest in pursuing an AGI and that these may be too expensive and time-consuming for most private entrepreneurs.