In this thesis, I develop two different stochastic real options models for two different financial applications, R&D (Research and Development) race and M&A (Mergers and Acquisitions) competition.

In the first part of the thesis, I consider a two-firm stochastic control model with finite time horizon for a mixed duopoly R&D race between the profit-maximizing private firm and welfare-maximizing public firm. In this model, the stochastic control variable is taken to be the private firm’s rate of R&D expenditure and the hazard rate of success of innovation has dependence on the R&D effort and knowledge stock. Given the fixed R&D effort of the public firm, the optimal control is determined so as to maximize the private firm’s value function subject to market uncertainty arising fro...[ Read more ]

In this thesis, I develop two different stochastic real options models for two different financial applications, R&D (Research and Development) race and M&A (Mergers and Acquisitions) competition.

In the first part of the thesis, I consider a two-firm stochastic control model with finite time horizon for a mixed duopoly R&D race between the profit-maximizing private firm and welfare-maximizing public firm. In this model, the stochastic control variable is taken to be the private firm’s rate of R&D expenditure and the hazard rate of success of innovation has dependence on the R&D effort and knowledge stock. Given the fixed R&D effort of the public firm, the optimal control is determined so as to maximize the private firm’s value function subject to market uncertainty arising from the stochastic profit flow of the new innovative product. Our R&D race model also incorporates the impact of input and output spillovers. We use two different numerical approaches to solve the Hamilton-Jacobi-Bellman (HJB) governing equation. In the first partial differential equation (PDE) approach, we apply the Bellman optimality condition to construct the HJB equation of the stochastic control model, and finite difference schemes together with policy iteration procedure are constructed for the numerical solution of the value function and optimal control of R&D expenditure of the private firm based on Leung and Kwok (2014). On the other hand, in the second approach, we extend the application of Markov chain approximation (MCA) approach (Kushner, 2001) after taking certain special precautions. Based on the reliable and well-matched numerical results from both approaches, we conduct various sensitivity tests with varying model parameters to analyze the effects of input spillover, output spillover and knowledge stock on the optimal control policies and the value function of the profit-maximizing private firm.

In the second part of the thesis, I develop a stochastic signaling game model for M&A competition under asymmetric information in real options frameworks. In this model, there are three firms in the market, one target firm and two bidder firms of different types, high type and low type. We incorporate the asymmetric information feature into the model settings of Morellac (2005) by letting the synergy factor to be the private information of the bidder firm, which is positively related to its quality type. The less informed target firm does not know the quality type of the bidder so that the merger surplus, as proxied by the synergy factor, cannot be estimated accurately. However, the target firm may still convey information about bidder’s quality type by observing bidder’s offer on merger timing and terms and thus update its belief on the synergy factor. With the inclusion of asymmetric information, we introduce a classic concept called Perfect Bayesian equilibrium (PBE) and derive the corresponding necessary and sufficient conditions for the two types of PBE, separating and pooling equilibrium. Based on those criteria, we analyze the characteristics of the optimal strategies adopted by different types of bidder firms under various market conditions and study the effects of asymmetric information on M&A strategies, as well as each firm’s merger surplus.