The valuation approach to real learning options under fuzzy-stochastic uncertainty

Abstract Asset and company valuation is a crucial topic in financial management, and the importance of the information gathering (the learning aspect) is increasing due to an innovation acceleration in the economy. The real learning options are sequential options with a usual market uncertainty and technical uncertainty, allowing for the modelling of the learning process. Low frequency data, subjectivity and the uncertainty of prediction in some cases mean that data can be determined only vaguely, expressed by a fuzzy-random distribution and fuzzy sets. This paper’s objective is to develop and verify the complete fuzzy-stochastic real learning option (CFSRLO) valuation model in a discrete time. Input data are given both the fuzzy-random distribution (the underlying cash-flow development, technical probability) and the fuzzy numbers (the continuum value, risk-free rate, risk rate, switching cost). The T-numbers, the Decomposition (resolution) principle, and $$\varepsilon -cut$$ are the essentials of the model’s construction. A stylised example presenting the case of technological development with learning and switching costs is presented. The influence of input vagueness via the incomplete fuzzy-stochastic real learning option model and the crisp-stochastic real learning option model is investigated. The contribution and novelty of the paper consist in the development and verification: the complete fuzzy-stochastic real learning option model, including a new aspect of information gathering (learning); completeness, because all input data are stated as fuzzy numbers; investigating a model robustness given by the vagueness of input data; the proposed model generalisation, which is applicable for various real learning option application types. The developed model can be applied in new product realisation conditions, R&D development, investment outlay, and resource extraction, especially in energy, pharmaceutical, mining, machinery, IT sectors and so on. The resulting fuzzy-stochastic real learning option value can be used for a sensitivity analysis of input data on a final value, used for finding out optimistic, middle and pessimistic solutions at a given aspiration level, and explored for the vagueness of optimal behaviour and control in managerial decisions.