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Faculty
Shreve
Steven E. Shreve, Orion Hoch Professor of Mathematical Sciences
Ph.D., University of Illinois
E-mail: shreve AT cmu DOT edu
Office: Wean Hall 6216
Phone: 412-268-8484
Personal web site

Research:

Shreve's recent research has followed two tracks. The _rst has been problems in financial mathematics, including models for derivative securities, utility maximization (especially in the presence of transaction costs), optimal execution of large financial transactions, and the principal agent problem of how a bank should compensate its traders. In all these cases, continuous-time models using stochastic calculus are constructed and analyzed.

A second activity has been modeling of queueing systems in heavy traffic when tasks have deadlines for completion. Although queues are intrinsically discrete-event systems, when in heavy traffic, the queue lengths can profitably be approximated by diffusions. If tasks have attributes, such as lead times until deadlines expire, the approximation is a measure-valued diffusion. In a series of papers with multiple co-authors, Shreve has determined the limiting measure-valued diffusion processes obtained in a variety of queueing systems.

These two threads have recently come together in the construction of diffusion approximations for limit-order books that govern trading on electronic exchanges. This is ongoing work with John Lehoczky of the CMU Department of Statistics and Ph.D. advisee Christopher Almost.


Selected Publications:

  • Asymptotic analysis for optimal investment and consumption with transaction costs (with K. Janecek), Finance and Stochastics 8, 181-206, 2004.
  • Satisfying convex risk limits by trading (with K. Larsen, T. Pirvu and R. Tutuncu), Finance and Stochastics 9, 177-196, 2005.
  • A two-person game for pricing convertible bonds (with M. Sirbu), SIAM Journal on Control and Optimization 45, 1508--1639, 2006.
  • Accuracy of state space collapse for earliest-deadline-first queues (with L. Kruk and J. Lehoczky), Annals of Applied Probability 16, 516-581, 2006.
  • An explict formula for the Skorokhod map on [0,a] (with L. Kruk, J. Lehoczky and K. Ramanan), Annals of Probability, to appear.