Let and be two independent fractional Brownian motions with respective indices and. In this paper, we consider their intersection local time and show that is differentiable in the spatial variable if. We introduce the so-calledhybrid quadratic covariation When, we construct a Banach spaceof measurable functions such that the quadratic covariation exists in and for all. Whena similar result is proved to hold for all Hölder functions of order

We consider pricing of exotic variance swaps and timer option written on the discretely sampled realized variance of an underlying asset under stochastic volatility models. Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. Thanks to the analytical tractability of the joint moment generating functions of the affine models, we manage to derive closed form analytic formulas for variance swap products with corridor features.

学术报告报告人:郁培教授(加拿大西安大略大学)题目： Impact of Delay on HIV-1 Dynamics of Fighting a Virus with Another Virus时间：2014年10月28日(星期二)上午10：00—11：00地点：致远楼105欢迎各位参加

In this talk, we not only want to decreases the difficulty of constricting the multisplitting of the coefficient matrix, but also release the constrains to the weighting matrices. We present two optimization models to modify parallel multisplitting iteration methods for solving positive definite (Hermitian or non-Hermitian) linear systems.

对于对称矩阵特征值问题， 我们详细而深入地讨论了块最速下降方法的多项式预处理 及其相应的收敛性质；提出了修正雅可比共轭预处理梯度方法，并研究了其代数性质和数 值行为。

In this lecture, we shall consider the mean field equation as an integrable system. Recently I and my collaborators have developed a theory to study the mean field equation. I will survey a part of this theory and show at the simplest situation how modular forms would be connected with the PDE.

We will discuss three aspects of the application of scientific methods to finance: (1) Investment (2) Derivatives (3) Risk Management. Although more advanced tools, such as stochastic differential equations, Monte Carlo simulation, psychology, statistical inference, optimization, and functional analysis may be needed to study these topics, only high school mathematics will be used in the talk. We aim at giving some concrete examples in these topics, to inspire interests among the general public. In particular, we will focus on three examples: (1) Optimal portfolio choices, e.g. Kelly and Merton criteria. (2) The binomial model for option pricing. (3) Axioms for risk measures.

Introduced by Borcherds, vertex operator algebra is a new algebra object arising from both mathematics and physics. In this expository talk, we will discus the origins and recent developments of vertex operator algebra. In particular, we will present a connection between vertex operator algebras and the modular forms.