AMC-SS: Mathematical Finance and Partial Differential Equations Conference - November 2, 2012

研究者和他的同事于2012年11月2日在罗格斯大学组织了“数学金融和偏微分方程会议”。线性和非线性偏微分方程解决数学金融基本问题的方法提供了共同的主题，这是受邀和贡献会议演讲者演讲的基础。Almgren和Guo将Hamilton-Jacobi-Bellman方程和随机控制应用于订单簿和交易的有效管理。Levendorskii和Nistor对美式期权定价问题中偏微分方程数值解的先进方法进行了研究。Hobson考虑了复杂期权定价的稳健方法。Keller-Ressel描述了仿射随机波动模型及其推广，而Pop则探索了将Gyongy定理扩展到具有无界系数的退化Ito过程的情况。Mazzeo考虑了数学生物学中的退化扩散过程和相关的偏微分方程。proteter讨论了概率论在金融泡沫中的应用。Zitkovic描述了他在投资组合理论和不完全市场方面的工作。本次会议的目的是根据演讲者讨论的主题开展学术和行业研究合作。会议参与者来自学术数学研究界和金融工程行业。参与者之间的互动鼓励思想的交流和知识的转移，并导致学术研究人员确定未来的研究问题和解决这些问题的可能方法。金融工程行业代表的参与确保了衍生证券定价、风险管理和交易方面的实际问题被介绍给具有应用数学相关专业知识的学术研究人员。行业应用包括改进控制模型风险的方法，更好地了解金融泡沫的起源，以及改善个人和养老基金的资产和投资组合管理。学术研究人员的参与确保了最新的学术研究和方法被描述给金融工程的从业者。来自学术界和工业界的研究人员的演讲促进了数学金融和偏微分方程作为纯数学和应用数学博士生的研究学科。会议资料发布在网站http://www.finmath.rutgers.edu/mfpde2012/上。

FeehanDMS-1237722 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 http://www.finmath.rutgers.edu/mfpde2012/.