A generalized real option pricing method of R&D investments: jump diffusion and external competition

ABSTRACT

Numerous studies have assessed Research and Development (R&D) investment using the real option pricing approach. This paper proposes a more general real option pricing method that both considers the specificity of R&D investment (such as uncertainty) and the R&D investment opportunity of a business in a market environment with external competitors. Specifically, we adopt a jump diffusion model to evaluate R&D investments that incorporate the uncertainties of these activities. The model values a pioneer's R&D investment opportunity allowing the chance that competitors may enter the market and the project value may vary with time. By construction and analysis of the model, we then analyse the optimal timing to realize profit on an investment. Overall, this model should facilitate a more comprehensive evaluation for R&D investments.     

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.      

Stochastic versus mean square stability in continuous time linear infinite Markov jump parameter systems

We deal with linear systems with Markovian Jump Parameters (LSMJP). Most of the literature on this matter adopts a finite state space for the Markov chain. In this paper we focus on the countably infinite state space case showing that, unlike the finite state space case, two important concepts in optimal control theory, namely, stochastic stability (SS) and mean square stability (MSS) are no longer equivalent in this setting.     

On optimal periodic dividend strategies in the dual model with diffusion

The dual model with diffusion is appropriate for companies with continuous expenses that are offset by stochastic and irregular gains. Examples include research-based or commission-based companies. In this context, Bayraktar et al. (2013a) show that a dividend barrier strategy is optimal when dividend decisions are made continuously. In practice, however, companies that are capable of issuing dividends make dividend decisions on a periodic (rather than continuous) basis.In this paper, we consider a periodic dividend strategy with exponential inter-dividend-decision times and continuous monitoring of solvency. Assuming hyperexponential gains, we show that a periodic barrier dividend strategy is the periodic strategy that maximizes the expected present value of dividends paid until ruin. Interestingly, a ‘liquidation-at-first-opportunity’ strategy is optimal in some cases where the surplus process has a positive drift. Results are illustrated.     

A model for speculation in a dynamic economy

The paper deals with speculation strategies in a dynamic economy, where “speculation” means participating in a market with the intention to gain a reward by first buying an item and thereafter selling it at a possibly higher price. By assuming that the states of the economy form a Markov chain the problem is modeled as a discrete time Markov decision process. The optimal strategies (which are pairs of stopping times) are identified. Under quite general conditions the optimal rule for the selling process turns out to be a control limit policy in both state of economy and time. Techniques for the computation of optimal strategies are presented; some numerical examples are also discussed. For a static economy closed-form solutions are given     

Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs

In this paper we consider the dividend payments and capital injections control problem in a dual risk model. Such a model might be appropriate for a company that specializes in inventions and discoveries, which pays costs continuously and has occasional profits. The objective is to maximize the expected present value of the dividends minus the discounted costs of capital injections. This paper can be considered as an extension of Yao et al. (2010), we include fixed transaction costs incurred by capital injections in this paper. This leads to an impulse control problem. Using the techniques of quasi-variational inequalities (QVI), this optimal control problem is solved. Numerical solutions are provided to illustrate the idea and methodologies, and some interesting economic insights are included.