TY - JOUR T1 - Modelling and Computation for the Valuation of Two-Period $R\&D$ Projects by Option Games AU - Zhang , Jiayue AU - Wang , Junlin AU - Wang , Xinyu JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 957 EP - 979 PY - 2019 DA - 2019/06 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0215 UR - https://global-sci.org/intro/article_detail/aamm/13196.html KW - $R\&D$ investment project, option game, compound American option, fitted finite volume method. AB -
In $R\&D$ investment projects, the value and the flexibility of investments are investigated by real option models, while the competition among the investors are mainly analyzed by the game theory. In this paper, we propose an option game model to analyze the case in which two firms invest the same project during a period of time. The firm taking the initiative, the leader, achieves more market shares, whereas the follower gains some investment information from the leader. We apply the fitted finite volume method and the power penalty method in order to get the solution of the option game model. Several managerial results including the payoffs and the effects of parameters are also discussed. Finally, by comparing the compound American option with the European one, we find the former more suitable for the analysis of $R\&D$ investment projects.