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We analyse how market price and policy uncertainty, in the form of random provision or retraction of a subsidy, interact to affect the optimal time of investment and the size of a renewable energy (RE) project that can be completed in either a single (lumpy investment) or multiple stages (stepwise investment). The subsidy takes the form of a fixed premium on top of the electricity price, and, therefore, investment is subject to electricity price uncertainty. We show that the risk of a permanent retraction (provision) of a subsidy increases (decreases) the incentive to invest, yet lowers (raises) the amount of installed capacity, and that this result is more pronounced as the size of the subsidy increases. Additionally, we show that increasing the number of policy interventions lowers the expected value of a subsidy and the size of the project. Furthermore, we illustrate that, although an increase in the size of a subsidy lowers the relative value of the stepwise investment strategy, the expected value of a lumpy investment strategy is still lower than that of stepwise investment.

Cybersecurity has become a key factor that determines\ud the success or failure of companies that rely on information\ud systems. Therefore, investment in cybersecurity is an important\ud financial and operational decision. Typical information technology\ud investments aim to create value, whereas cybersecurity investments\ud aim to minimize loss incurred by cyber attacks. Admittedly,\ud cybersecurity investment has become an increasingly complex\ud one since information systems are typically subject to frequent\ud attacks, whose arrival and impact fluctuate stochastically. Further,\ud cybersecurity measures and improvements, such as patches,\ud become available at random points in time making investment\ud decisions even more challenging.\ud We propose and develop an analytical real options framework\ud that incorporates major components relevant to cybersecurity\ud practice, and analyze how optimal cybersecurity investment decisions\ud perform for a private firm. The novelty of this paper is that\ud it provides analytical solutions that lend themselves to intuitive\ud interpretations regarding the effect of timing and cybersecurity\ud risk on investment behavior using real options theory. Such\ud aspects are frequently not implemented within economic models\ud that support policy initiatives. However, if these are not properly\ud understood, security controls will not be properly set resulting\ud in a dynamic inefficiency reflected in cycles of over or under\ud investment, and, in turn, increased cybersecurity risk following\ud corrective policy actions.\ud Results indicate that greater uncertainty over the cost of\ud cybersecurity attacks raises the value of an embedded option\ud to invest in cybersecurity. This increases the incentive to suspend\ud operations temporarily in order to install a cybersecurity patch\ud that will make the firm more resilient to cybersecurity breaches.\ud Similarly, greater likelihood associated with the availability of a\ud cybersecurity patch increases the value of the option to invest in\ud cybersecurity. However, absence of an embedded investment option\ud increases the incentive to delay the permanent abandonment\ud of the company’s operation due to the irreversible nature of the\ud decision

Risk aversion typically erodes the value of an investment opportunity, often increasing the incentive to delay investment. Although this may be true when the decision maker has discretion only over the timing of investment, any additional discretion over the capacity of a project may lead to different results. In this paper, we extend the traditional real options approach by allowing for discretion over capacity while incorporating risk aversion and operational flexibility in the form of suspension and resumption options. In contrast to a project without scalable capacity, we find that increased risk aversion may actually facilitate investment because it decreases the optimal capacity of the project. Finally, we illustrate how the relative loss in the value of the investment opportunity due to an incorrect capacity choice may become less pronounced with increasing risk aversion and uncertainty.