COMMERCIAL AND INDUSTRIAL MATHEMATICS

September 18, 2014

Seminar Series on Quantitative Finance - May 26, 2004

Abstracts

Eduardo Schwartz, Anderson School of Management, UCLA
A Model of R & D Valuation and the Design of Research Incentives
We develop a real options model of R&D valuation, which takes into account the uncertainty in the quality of the research output, the time and cost to completion, and the market demand for the R&D output. The model is then applied to study the problem of pharmaceutical under-investment in R&D for vaccines to treat diseases affecting the developing regions of the world. To address this issue, world organizations and private foundations are willing to sponsor vaccine R&D, but there is no consensus on how to administer the sponsorship effectively. Different research incentive contracts are examined using our valuation model. Their effectiveness is measured in the following four dimensions: cost to the sponsor, the probability of development success, the consumer surplus generated and the expected cost per person successfully vaccinated. We find that, in general, purchase commitment plans (pull subsidies) are more effective than cost subsidy plans (push subsidies), while extending patent protection is completely ineffective. Specifically, we find that a hybrid subsidy constructed from a purchase commitment combined with a sponsor co-payment feature produces the best results in all four dimensions of the effectiveness measure.

John Chadam, University of Pittsburgh
Early exercise boundaries: Numerical and analytical approximations
We provide several fast and accurate numerical and analytical approximations for the location of early exercise boundaries. The main ideas will be presented in the simplest case of the American put option on a geometric Brownian motion. We will also mention how the techniques can be carried over to a wide class of underlyings and payoffs (e.g., jump-diffusions, interest rate products, etc.). The presentation will be made in the partial differential equation framework using methods from the free boundary literature. Various parts of this work are joint with Xinfu Chen (Pittsburgh), Lishang Jiang (Shanghai), David Lozinski (TD Bank, Toronto), David Saunders (Pittsburgh), Rob Stamicar (RiskMetrics, New York) and Weian Zheng (Irvine).

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