Mathematical analysis underlies all of my work. Given that modelling and analysis are fundamental to my research approach, the level of abstraction and formalism in my writing would appear high to business people. By contrast, my work would appear applied to mathematicians. With just a few exceptions, I view my research as a mixture.
Four factors appear in nearly all of my publications. First, my research concerns the impact of uncertainty upon economic decision making. Second, the issues addressed concern dynamic phenomena and necessitate the use of a multi-period framework. Third, the issues are explicated by finding the qualitative structure of the decision maker's optimal policy. Fourth, discerning the impact of changes in the problem parameters upon the optimal policy is a major objective of the analysis: the papers effect a comparative statics analysis. With a few exceptions, each paper contains a model designed to address a specific economic issue of Operations Research phenomenon. In the exceptions either the papers introduce a general technique useful in analyzing a wide variety of models, or the principal goal of the papers is to provide and verify the most general conditions under which an optimal policy exists in a Markov decision process.
My two streams of research are bridged by common techniques but separated by subject matter and, to a lesser extent, by emphasis on technique. Because the issues I address deal with sequential decision making in the presence of uncertainty, dynamic programming is the principal tool employed in my analyses. Dynamic programming is the linchpin providing the strongest and most consistent connection between my various publications. The technique of dynamic programming was born in Operations Research, the field in which I was trained to do research. A number of researchers, including myself, have imported this tool to economics. My knowledge of and facility with dynamic programming coupled with my interests in economics have found application in the fields of information economics and labor economics (where search theory was first used in economics), industrial organization, and R&D (a subfield of industrial organization).
In retrospect it is apparent that search
theory is a broad paradigm with applications extending far beyond the initial
economic application to labor markets. Most economists would argue that
the literature on R&D races and other streams within industrial organization
are not part of the search literature, but it seems clear to me that the
mathematical structures underpinning the modelling efforts are all but
identical. Relatedly, the work in queueing optimization and the older work
in stochastic inventory theory possess a mathematical structure which is
close to that of the search paradigm. This reveals more coherence in my
research programme than may be suggested by the diversity of topics adressed
by this research.
