Integrating Probability and Possibility Theory: A Novel Approach to Valuing Real Options in Uncertain Environments

The article presents a new method for evaluating investment projects in uncertain conditions, assuming that uncertainty may have been two origins: aleatory (related to randomness) and epistemic (due to incomplete knowledge). Epistemic uncertainty is rarely considered in investment analysis which can result in undervaluing the future opportunities and risks. Our approach utilizes the Datar-Mathews Method (DM Method) to gather relevant information regarding the potential value of real option. By combining probabilistic and possibilistic approaches, proposed valuation model incorporates hybrid Monte Carlo simulation and a random-fuzzy Geometric Brownian Motion, considering the interdependence between parameters. The result of the hybrid simulation is a pair of upper and lower cumulative probability distributions, known as a p-box, which represents the uncertainty range of the Net Present Value (NPV). We propose three transformations of the p-box into a subjective probability distribution, which allow decision-makers to incorporate their subjective beliefs and risk preferences when performing real option valuation. Thus, our approach allows the combination of objective available information about valuation of investment with the decision-maker's attitude in front of partial ignorance. To demonstrate the effectiveness of our approach in practical scenarios, we provide a numerical illustration that clearly showcases how our approach delivers a more precise valuation of real options.