Real Options with Incomplete Information and Multi-dimensional Random Controls

In this paper we provide a real (investment) options ́ valuation method with controls that capture managerial intervention and learning (exploration, R&D, advertising, marketing research, etc.). In contrast to the standard wait-and-see approach of the real options literature, we assume that managers possess the ability to intervene either for value enhancement, or for information acquisition, and of course they wish to do so optimally. We assume the presence of multiple stochastic state-variables that follow Geometric Brownian motion (GBM), or jump-diffusion processes. Activated controls can affect several or all of the state-variables, and the outcome of control activation is random. For the case first of GBM processes, an analytic solution is provided to value the real claim in the presence of such multi-dimensional controls, and a Markov-chain numerical method is demonstrated for more complex applications. The method of random controls is similarly extended to the case where the statevariables follow jump-diffusion processes, with multiple classes of jumps. An analytic solution is provided, and again a Markov-chain numerical method is demonstrated. Neglecting the effect of such actions, causes a serious underestimate of the value of real options and leads to erroneous decision making.