We develop and analyze a model of a multi-stage investment project that captures many features of R&D ventures and start-up companies. An important feature these problems share is that the firm learns about the potential profitability of the project throughout its life, but that research and development effort itself is only resolved through additional investment by the firm. In addition, the risks associated with the ultimate cash flows the firm realizes on completion of the project have a systematic component, while the purely technical risks are idiosyncratic. Our model captures these different sources of risk, and allows us to study their interaction in determining the risk premia earned by the venture during development. Our results show that the systematic risk, and the required risk premium, of the venture are highest early in its life, and decrease as it approaches completion, despite the idiosyncratic nature of the technical risk.

Valuation and Return Dynamics of New Ventures

A dynamic model of a multistage investment project that captures many features of research and development (R&D) ventures and start-up companies is developed. An important feature these problems share is that firms learn about the potential profitability of the project throughout its life, but that technical uncertainty about the R&D effort is only resolved through additional investment. Consequently the risks associated with the ultimate cash flows have a systematic component even while the purely technical risks are idiosyncratic. Our model captures these different sources of risk and allows us to study their interaction in determining the value and risk premium of the venture. Copyright 2004, Oxford University Press.

/pdf/valuation-and-return-dynamics-of-new-ventures-3gtq3gytk4.pdf

Consider a continuous-time Markov chain evolving in a random environment. We study certain forms of interaction between the process of interest and the environmental process, under which the stationary joint distribution is tractable. Moreover, we obtain necessary and sufficient conditions for a product-form stationary distribution. A number of examples that illustrate the applicability of our results in queueing and population growth models are also included.

/pdf/generalized-product-form-stationary-distributions-for-markov-5ahrxva0rj.pdf

Generalized product-form stationary distributions for markov chains in random environments with queueing applications

Based on a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts in the form of a self-exciting point process, a bank can control the arrival intensity of ...

Dynamic Credit-Collections Optimization

The paper considers a race among multiple firms that compete over the development of a product. The first firm to complete the development gains a reward, whereas the other firms gain nothing. Each firm decides how much to invest in developing the product, and the time it completes the development is a random variable that depends on the investment level. The paper provides a method for explicitly computing a unique Nash equilibrium, parametrically in the interest rate; for a given interest rate, the Nash equilibrium is determined in time that is linear in the number of firms. The structure of the solution yields insights about the behavior of the participants. Furthermore, an explicit expression for a unique globally optimal solution is obtained and compared to the unique Nash equilibrium.

A Stochastic Competitive R&D Race Where “Winner Takes All”

Our study examines a stochastic R&D model with flexible termination time and without rivalry. Specifically, we assume a stochastic relationship between expenditures rate and the project's status.Furthermore, the termination time of the project is incorporated into the R&D model as a decision variable by allowing the controller to 'sell' the obtained technology from the project at any point of time. The proposed framework extends the classical approach in the R&D literature. The main purpose of our study is to determine the optimal stopping time of the project and to characterize qualitatively the firm's expenditure strategy. We show that under certain realistic conditions, the optimal stopping strategy is a control limit policy. Furthermore, the research effort increases monotonically over the development time of the project.

M. J. M. Posner

Papers

Optimal R&D programs in a random environment