Modern financial mathematics evolved in the past decades out of the need to manage risk with financial instruments like derivative contracts. After a brief historical review of how this subject started and has evolved I will discuss current issues in the quantification and management of risk in financial markets. Until recently, risk assessment models did not consider seriously the effects of inter-connectedness of financial agents and markets, and the way risk diversification impacts the overall stability of markets. I will discuss this issue and more generally how the stability of markets is affected by different patterns of trading.
George C. Papanicolaou is currently the Robert Grimmett Professor in Mathematics at Stanford University. Besides his former focus on the analysis of waves and diffusion in inhomogeneous or random media, his recent research interests also include financial mathematics, especially the use of asymptotics for stochastic equations in analyzing complex models of financial markets and in data analysis. In 1987, the University of Athens conferred an Honorary Doctor of Science on Papanicolaou. In 2000, he became a Fellow of the American Academy of Arts and Sciences and he was elected to the U.S. National Academy of Sciences. Papanicolaou was invited plenary speaker at multiple international congresses, among others at the SIAM 50th anniversary meeting in 2002 and at the International Congress of Industrial and Applied Mathematics in 2003. In 2006, he received the SIAM von Neumann Prize in recognition of his wide-ranging work on analytic and stochastic methods and their application to the modeling of phenomena in the physical, geophysical, and financial sciences. In 2010 he received the William Benter Prize in Applied Mathematics. In 2011 he was the Gibbs lecturer of the American Mathematical Society. The University of Paris Diderot conferred on him the degree Doctor Honoris Causa in 2011.