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Math Faculty

William J. Hrusa
Professor of Mathematical Sciences, Dr. Hrusa earned his Ph.D. from Brown University.  His main areas of research are in partial differential equations, integral equations, and calculus of variations with particular emphasis on problems that arise in continuum mechanics. Current research is focused on Lavrentiev’s phenomenon in the calculus variations, i.e. with situations in which the infimum for a given variational problem is sensitive to the precise degree of regularity that is assumed for the competing functions. A major goal is to understand if this phenomenon can occur for realistic problems in nonlinear elasticity.

Dmitry Kramkov
Mellon College of Science Professor of Mathematical Finance, Professor Kramkov earned his Ph.D. from the Steklov Mathematical Institute in Moscow in 1991. His current research is mainly focused on topics in mathematical finance such as equilibrium, dynamic game theory, option pricing theory, and optimal investment. In 1996 he received a prize of the Second European Congress of Mathematics in Budapest for his research on statistics and mathematical finance. From 1997 to 2000 Dr. Kramkov worked for Tokyo-Mitsubishi International in London, where he was the Acting Head of Research and Product Development. His main responsibility was the evaluation of complex derivative contracts. Dr. Kramkov currently serves as a member of the Executive Board of the Bachelier Finance Society and as an Associate Editor of the journal of Finance and Stochastics. He has an affiliation with the University of Oxford, where he is a member of Man-Oxford Institute for Quantitative Finance.

Kasper Larsen
Associate Professor of Mathematical Sciences with a background in Mathematical Economics from the University of Southern Denmark. Dr. Larsen's research interests are mainly how mathematical tools can be applied to solve problems from finance and economics. The main research focus is utility theory and various applications hereof such as model stability and equilibrium price formation. His work has been published in journals such as the Mathematical Finance, Finance and Stochastics, Annals of Applied Probability, and Journal of Economic Theory.

Roy A. Nicolaides
Professor of Mathematical Sciences, Ph.D. from the University of London. Professor Nicolaides' research and teaching interests include applications of partial differential equations to mathematical finance and other fields.  He serves or has served on the editorial boards of the Journal of Computational Finance, the SIAM Journal of Scientific Computing, the Journal of Computational Fluid Dynamics, and other journals. Professor Nicolaides teaches the MSCF course on numerical methods for partial differential equations, which he has done since the program began in 1994.

Scott Robertson
Assistant Professor of Mathematical Sciences, Professor Robertson earned his Ph.D. from Boston University. His research focuses on using the theory of Large Deviations to solve problems of optimal investment and options pricing in Mathematical Finance.  Prior to attending graduate school, Professor Robertson worked for four years as an analyst in the Fixed-Income research departments at both Citigroup and Fidelity Investments. Professor Robertson's papers have been published in Mathematical Finance, Finance and Stochastics, and the Annals of Applied Probability.

Steven Shreve
Orion Hoch and University Professor of Mathematical Sciences and member of the MSCF Steering Committee. Professor Shreve earned his Ph.D. in 1977 from the University of Illinois. His research and teaching interests range from capital asset pricing models to various aspects of mathematical finance, including studying the effect of transaction costs and unknown volatility on option prices and the pricing and hedging of exotic options. Dr. Shreve is past-President of the Bachelier Finance Society. In 1994, Dr. Shreve was one of the founders of the Carnegie Mellon Master's program in Computational Finance. Dr. Shreve serves as Advisory Editor of the journal, "Finance and Stochastics." He has co-authored a number of books, including "Brownian Motion and Stochastic Calculus" and "Methods of Mathematical Finance." He has written a two-volume work based on his teaching in the MSCF program, "Stochastic Calculus for Finance."

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