Partial differential equations, probability, and analytical methods are fundamental tools in the modeling and description of financial markets. The purpose of this meeting is to showcase new methods, directions and the most recent research in partial differential equations, probability, stochastic control, numerical analysis, and their application to mathematical finance. Invited presentations by leading academic and industry researchers highlight the latest research in the application of partial differential equations to option pricing, portfolio optimization, risk management, and high-frequency trading. Their presentations focus on degenerate-elliptic and degenerate-parabolic variational equations and inequalities for stochastic volatility models in finance; free-boundary value problems; stochastic control and the Hamilton-Jacobi-Bellman equation; non-linear partial differential equations in finance; stochastic optimal control, high-frequency finance and algorithmic trading; and numerical solution of partial-integro differential equations and inequalities. The invited talks are complemented by presentations on these themes contributed by promising young researchers.
The conference will help foster academic and industry research collaborations; introduce industry problems to academic researchers; introduce academic research and methods to industry practitioners; facilitate scientific networking opportunities for junior practitioners and graduate students; and foster mathematical finance and partial differential equations as a research discipline for Ph.D. students in pure and applied mathematics. We especially welcome participation by women, minorities, and other underrepresented groups, as well as students and junior researchers.
in December 10, 2010 and November 4, 2011 at Rutgers University, New Brunswick, New Jersey. NSF support facilitated participation by students, junior researchers, and traditionally under-represented groups, including women and minorities. Our conferences and the research carried out by the PI during the years these conferences were held emphasized the role in financial engineering played by degenerate-elliptic and degenerate-parabolic partial differential equations, degenerate stochastic processes, extensions of Gyongy's mimicking theorem, numerical solution of partial differential equations, numerical solution of obstacle problems, and American-style option pricing for degenerate diffusion processes. While Monte Carlo methods are in common use for pricing and risk management models in industry, nevertheless, they cannot compete with partial differential equation methods for speed and accuracy in low-dimensional problems, pricing and hedging American-style options, or in recent applications of stochastic control (Hamilton-Jacobi-Bellman equation) to finance. Despite the advantages of partial differential equations, many industry practitioners are unaware of the latest academic research in their numerical solution or the deeper theoretical issues surrounding degenerate partial differential equations or Markov processes, with many firms still using outdated and unsatisfactory methods (such as trees). Conversely, many academic researchers in partial differential equations and probability are unaware of the wealth of deep and challenging mathematical problems motivated by industry developments. Our conferences helped develop academic and industry research collaborations; introduced industry problems to academic researchers; introduced academic research and methods to industry practitioners; facilitated scientific networking opportunities for junior practitioners, postdoctoral researchers, and graduate students; and fostered mathematical finance and partial differential equations as a research discipline for Ph.D. students in pure and applied mathematics.
