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| Image courtesy of Prof. Gennady Samorodnitsky |
Rick Durrett (Department of Mathematics) works on a variety of probability problems that arise from biology. For much of the last 20 years this has meant stochastic spatial models for ecological process, but for the last half dozen years his main inspiration has come from genetics. Durrett has written eight books. The last two, which are still in the process of being published by Cambridge University Press, are a research monograph: Random Graph Dynamics, and an introduction of probability for students who have had one semester of calculus: Elementary Probability for Applications.
Shane Henderson focuses on stochastic simulation, including generation of random variables, vectors, and processes. He works on increasing the efficiency of simulations through variance reduction techniques.
Robert Jarrow (Johnson Graduate School of Management) studies the applications of probability theory and stochastic calculus to mathematical finance. His current applications include the term structure of interest rates, credit risk, liquidity risk, and risk management theory.
Mark Lewis works on issues of stochastic control as they relate to discrete-time decision making under uncertainty. He has worked on the control of queues, inventory systems, financial decisions, and transportation routing issues. He has also made theoretical contributions to the theory of Markov decision processes under the discounted cost, average cost, and transient cost (bias) optimality criterion.
Narahari U. Prabhu is interested in probability theory and stochastic processes. He has worked on regenerative phenomena, fluctuation theory, Werner-Hopf factorization, Markov-renewal, and Markov-additive processes. He has had a long-standing interest in stochastic models for storage systems, queues, inventories, insurance risk, data communications, and transportation. He has also worked on inference and control and stochastic comparisons.
Philip Protter has long been interested in stochastic integration (most recently, he developed extensions of Ito’s formula). Additionally, he is interested with Monte Carlo methods in applications of Markov processes, and with numerical solutions of Backwards Stochastic Differential Equations and Forward-Backwards Stochastic Differential Equations. Related to Financial Engineering, he has made precise and rigorous the popular technique known as the "Longstaff-Schwartz algorithm.”
Sidney Resnick is interested in applications of extreme value theory, especially the subbranch of heavy tail analysis useful in network modeling, insurance, and finance. He seeks improved methods for detecting properties in measured data and models—methods that predict while coping with the difficulties of inferring properties usually beyond the range of the data.
Gennady Samorodnitsky works on stochastic models, particularly nonstandard ones, such as those with heavy tails and/or long-range dependence. He is interested in rare events and large deviations. Samorodnitsky is also interested in extremal behavior of stochastic models, and in scaling, self-similarity, and, more generally, fractal behavior of stochastic models. He works on time series and on random fields. Applications of his work involve finance, risk theory, and communication networks.
Michael Todd is interested in probabilistic analysis of algorithms such as the simplex method, an algorithm which is surprisingly effective for very-large-scale linear programming in spite of having worst-case exponential-time complexity. Todd has shown that a variant of the method has quadratic expected-iteration complexity under certain probability distributions on problem instances. He has also studied properties of linear programming problems under a variety of such distributions.
Stefan Weber works on applications of probability theory to mathematical finance. He is interested in credit, liquidity and operational risk, risk measures, optimal portfolio choice, and Monte Carlo methods. Mathematical techniques include stochastic analysis, dynamical systems, large deviations, interacting particle systems, and convex analysis.