The investigator and his colleagues organize the "Mathematical Finance and Partial Differential Equations Conference" November 2, 2012, at Rutgers University. Methods of linear and nonlinear partial differential equations to solve fundamental problems in mathematical finance provide the common theme that underlies presentations by the invited and contributing conference speakers. Almgren and Guo address applications of the Hamilton-Jacobi-Bellman equation and stochastic control to efficient management of order books and trading. Research of Levendorskii and Nistor concerns advanced methods for numerical solution of partial differential equations arising in American-style option pricing problems. Hobson considers robust methods for pricing complex options. Keller-Ressel describes affine stochastic volatility models and their generalizations while Pop explores extensions of Gyongy's theorem to the case of degenerate Ito processes with unbounded coefficients. Mazzeo considers degenerate diffusion processes and associated partial differential equations in mathematical biology. Protter discusses applications of probability theory to bubbles in finance. Zitkovic describes his work on portfolio theory and incomplete markets.
The purpose of this conference is to develop academic and industry research collaborations based on the themes discussed by the speakers. Conference participants come from both the academic mathematical research community and the financial engineering industry. Interactions among the participants encourage cross-fertilization of ideas and transfer of knowledge and lead to identification of future research problems for academic researchers and of possible methods to solve them. The participation of representatives from the financial engineering industry ensures that practical problems in derivative security pricing, risk management, and trading are introduced to academic researchers with relevant expertise in applied mathematics. The industry applications include improved methods to control model risk, better understand the origins of financial bubbles, and improve asset and portfolio management for individuals and pension funds. The participation of academic researchers ensures that the latest academic research and methods are described to practitioners in financial engineering. Presentations by researchers from both academia and industry foster mathematical finance and partial differential equations as a research discipline for Ph.D. students in pure and applied mathematics. Conference materials are posted on the web at www.finmath.rutgers.edu/mfpde2012/.
