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We provide a review on quantitative methods for low-medium frequency trading and high frequency trading. For low-medium frequency trading, we review the different econometric estimators to extract a trend of a time series which is widely used in momentum strategies. We distinguish between linear and nonlinear models as well as univariate and multivariate filtering. For high frequency trading, we introduce a multivariate point process describing the dynamics of the Bid and Ask price of a financial asset. The point process is similar to a Hawkes process, with additional constraints on its intensity corresponding to the natural ordering of the best Bid and Ask prices. We study this process in the special case where the fertility function is exponential so that the process is entirely described by an underlying Markov chain including the constraint variable.

学 术 报 告题目： Spectral Asymptotics for Automorphic Forms报告人： Erez M. Lapid 教授（报告人简介：Erez M. Lapid是以色列希伯来大学数学研究所教授，在自守形式方面有杰出工作，应邀在印度举办的2010年国际数学家大会上作45分钟报告）时间：2014年4月18日10：00—11：00地点：致远楼102欢迎各位参加

This talk aims to extend the literature concerning four patterns of behavior exhibited by day traders and the impact on performance. Based on the Sample of data from day traders from the Taiwan stock index futures (TXF) by analyzing transaction records of each trader. We will discuss why some day traders are profitable and others are not. By examining the transactions at an individual level, patterns of behavior can be identified. One goal of this paper is to better understand what patterns of day traders’behavior produce any given performance.

学术报告报告人:寇春海教授(东华大学)题目：分数阶微积分与分数阶微分方程时间：2014年4月14日(星期一)下午3：00—4：00地点：致远楼10

报告人：Prof. Hao Xing (London School of Economics and Political Science, UK）题目： Portfolio Turnpikes in Incomplete Markets时间：2014年4月1日(星期二)下午4：00—5：30地点：数学系致远楼107欢迎各位参加

We consider a free boundary problem associated with the curvature dependent motion of planar curves in the upper half plane whose two endpoints slide along the horizontal axis with prescribed fixed contact angles. Our first main result concerns the classification of solutions; every solution falls into one of the three categories, namely, area expanding, area bounded and area shrinking types. We then study in detail the asymptotic behavior of solutions in each category. Among other things we show that solutions are asymptotically self-similar both in the area expanding and the area shriknking cases, while solutions converge to either a stationary solution or a traveling wave in the area bounded case. We also prove results on the concavity properties of solutions. This is a joint work with Hiroshi Matano, Chang-Hong Wu and Jong-Shenq Guo.

We study nonlinear advection-diffusion problems of the form u_t - u_{xx} + /beta u_x = f(u) with free boundaries x = h(t) and x = g(t). Such a problem may be used to describe the spreading of a biological or chemical species with the free boundaries representing the expanding fronts. The term /beta u_x represents an effect of advective environments. For logistic nonlinearity, it has been shown by Gu, Lin and Lou that the asymptotic spreading speeds of the two fronts h(t) and g(t) are different due to the advection term. In this paper, when the nonlinear function is a monostable, bistable or of combustion type, we give a much sharper estimate for the different spreading speeds of the fronts, and describe how the solution approaches a semi-wave when spreading happens. We develop new approaches and extend the result of Du, Matsuzawa and Zhou to the problem with an advection term.

Auslander-Reiten theory for finite dimensional algebras is well-established. There is also Auslander-Reiten theory for orders, but it seems no references which define AR-quivers for orders in non semi-simple algebras and study their shapes. I will explain how to construct almost split sequences for self-injective orders and introduce Heller lattices. Then, we show, in a simple example, the shape of components of stable AR-quiver that contain Heller lattices.