In this article we develop a model to analyze patent-protected R&D investment projects when there is (imperfect) competition in the development and marketing of the resulting product. The competitive interactions that occur substantially complicate the solution of the problem since the decision maker has to take into account not only the factors that affect her/his own decisions, but also the factors that affect the decisions of the other investors. The real options framework utilized to deal with investments under uncertainty is extended to incorporate the game theoretic concepts required to deal with these interactions. Implementation of the model shows that competition in R&D, in general, not only increases production and reduces prices, but also shortens the time of developing the product and increases the probability of a successful development. These benefits to society are countered by increased total investment costs in R&D and lower aggregate value of the R&D investment projects.

Under the assumptions of the Consumption-based Capital Asset Pricing Model (CCAPM), Pareto optimal consumption allocations are characterized by each agent's consumption process being adapted to the filtration generated by the aggregate consumption process of the economy. The wealth processes of the agents, however, are adapted to the finer filtration generated by aggregate consumption and the conditional distribution of future aggregate consumption. Therefore, in order to achieve pareto optimal consumption allocations, a sufficiently varied set of assets must exist such that any wealth process adapted to this finer filtration can be implemented by dynamically trading in that set of assets. We provide sufficient conditions for the existence of such a set of assets based on dynamically trading contingent claims on aggregate consumption. In addition, we give sufficient conditions for the existence of equilibria in a dynamically effectively complete market in which agents are only able to trade in contingent claims on aggregate consumption, the market portfolio of firms, and a (numeraire) zero-coupon bond. We demonstrate the role of short- and long-term contingent claims on aggregate consumption for the implementation of Pareto optimal allocations inthe presence of short- and long-term risks. In addition, in the presence of personal risks, we demonstrate the role of insurance contracts.

Kristian R. Miltersen, Klaus Sandmann, Dieter Sondermann, Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates, The Journal of Finance, Vol. 52, No. 1 (Mar., 1997), pp. 409-430

The authors derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero-coupon bonds. The crucial assumption is that simple interest rates over a fixed finite period that matches the contract, which the authors want to price, are log-normally distributed. Moreover, this assumption is shown to be consistent with the Heath-Jarrow-Morton model for a specific choice of volatility.

We derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero‐coupon bonds. The crucial assumption is that simple interest rates over a fixed finite period that matches the contract, which we want to price, are log‐normally distributed. Moreover, this assumption is shown to be consistent with the Heath‐Jarrow‐Morton model for a specific choice of volatility.

Kristian R. Miltersen, Eduardo S. Schwartz, Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates, The Journal of Financial and Quantitative Analysis, Vol. 33, No. 1 (Mar., 1998), pp. 33-59

We consider a dynamic trade-off model of a firm's capital structure with debt renegotiation. Debt holders only accept restructuring offers from equity holders backed by threats which are in the equity holders' own interest to execute. Our model shows that in a complete information model in which taxes and bankruptcy costs are the only frictions, violations of the absolute priority rule (APR) are typically optimal. The size of the bankruptcy costs and the equity holders' bargaining power affect the size of APR violations, but they have only a minor impact on the choice of capital structure.