This paper is devoted to propose a random fuzzy methodology in order to value R&D investments combining the stochastic approach with the fuzzy analysis. As it is commonly known, an R&D project is characterized by a sequential phase in which each phase gives to the manager the opportunity to realize or not the investment. So, in real option world, this opportunity can be analyzed as a compound American exchange option (CAEO). In this paper, the fuzzy approach is used to model two important parameters of R&D evaluation: the volatility of asset V and the opportunity costs of deferring project δvδv. Therefore, we present a γ-level of fuzzy prices of CAEO and the fuzzy mean value of CAEO using a pessimistic–optimistic weight.

The paper examines the stability of international environmental agreements (IEAs) in a dy- namic context where abatement levels are associated with the stock pollutant evolution. We underline two meaningful aspects of this matter. Firstly, we consider asymmetry among coun- tries, dividing them in two types: developed countries that have a considerable environmental awareness and developing ones that pay a less attention to environmental preservation. Sec- ondly, we introduce a positive externality in the cooperation where countries coordinate their R&D activities sharing the investments in order to avoid duplication of green activities. Other- wise, the non-cooperators support completely their R&D investments for clean technologies. These two aspects encourage the formation of stable coalitions till to determine conditions for which also the grand coalition is stable.

In this paper we show the applicability of the Least Squares Monte Carlo (LSM) in valuing R&D investment opportunities. As it is well known, R&D projects are made in a phased manner, with the commencement of subsequent phase being dependent on the successful completion of the preceding phase. This is known as a sequential investment and therefore R&D projects can be considered as compound options. Moreover, R&D investments often involve considerable cost uncertainty so that they can be viewed as an exchange option, i.e. a swap of an uncertain investment cost for an uncertain gross project value. In this context, the LSM method is a powerful and flexible tool for capital budgeting decisions and for valuing R&D investments. In fact, this method provides an efficient technique to value complex real investments involving a set of interacting American-type options.

This paper provides a real option methodology in order to value a pioneer’s R&D investment opportunity allowing for more potential competitors to enter in the market. To incorporate this competitive dimension, we assume that the pioneer may lose the “competitive dividends” if the real option is not exercised. According to Majd and pindyck (1987) (Journal of Financial Economics 18(1):7–27), in a real options context, “dividends” are the opportunity costs inherent in the decision to defer an investment project and so deferment implies the loss of project’s cash flows. Concerning this, Trigeorgis (1996) (Real Options: Managerial Flexibility and Strategy in Resource Allocation, The MIT Press, Cambridge, (1996) incorporates the preemption effect through the “competitive dividends” which are the cash flows that can be eroded by anticipated competitive arrivals. In particular way, we propose the valuation of a pioneer’s R&D investment assuming that the Development cost can be spent in two moments: t2 or t3 . If the Development cost is realized in t2 no firms enters in the market since the rivals’ R&D plan is not yet concluded otherwise, if the Development cost is delayed until time t3 waiting better market conditions, other rivals may enter in the market and so the opportunity costs, namely dividends, increase. Moreover, we analyze the optimal timing to realize the Development investment, i.e. we determine the conditions for which the pioneer prefers to invest the Development cost at time t2 or t3 .