We investigate the partial differential equation (PDE) for pricing interest derivatives in the multi-factor Cheyette Model, that involves time-dependent volatility functions with a special structure. The high dimensional parabolic PDE that results is solved numerically via a modified sparse grid approach, that turns out to be accurate and efficient. In addition we study the corresponding Monte Carlo simulation, which is fast since the distribution of the state variables can be calculated explicitly. The results obtained from both methodologies are compared to the analytical solution existing for bonds and caplets. Keywords: Cheyette Model, Gaussian HJM, Multi-Factor Model, PDE Valuation, Sparse Grid, Monte Carlo Simulation

Workshop on Geometry and TopologyOctober 14-16, 2011Department of Mathematics, Tongji UniversityScheduleOctober 14, Friday8:50-9:00 Opening ceremonyChair: Bian Baojun9:00-9:45 Zhang Weiping (Chern Institute, Nankai University)Dirac operators and vanishing theorems9:55-10:40 Ding Qing (Fudan University)Bounded Harmonic Functions on Riemannian Manifolds ofNonpositive CurvatureTea break (take grou...

报 告 人：徐兴旺 教授（国立新加坡大学数学系）报告题目： The Scalar Curvature Flow报告时间：2011年9月23日（周五）下午3：30-4:30报告地点：致远楼107室欢迎广大师生参加！2011-9-1

Abstract: The optimal portfolio selection problem is the fundamental optimization problem in finance – optimally balancing risk and return, with possible additional constraints. Unfortunately the classical optimization approach is very sensitive to estimation error, especially with respect to the estimated mean return, and the resulting efficient frontier may be of little practical value. Indeed it may be dangerous from a risk management point of view. A popular alternative, usually under the banner of “robust optimization” is ultra-conservative and, we argue, not really robust! In this sense it may also be of questionable practical value. We propose an alternative optimization approach – a CVaR optimization formulation that is relatively insensitive to estimation error, yields diversified optimal portfolios, and can be implemented efficiently. We discuss this promising approach in this talk and present strongly supportive numerical results.

报告人：徐洪坤教授（台湾中山大学西湾讲座教授，南非科学院院士）题目: Convex Relaxations for Recovering Sparse Signals with Noise时间：2011年9月1日(星期四)下午4：30—5：30地点：数学系致远楼107欢迎各位参加

报告人：Prof. Tzon-Tzer Lu（National Sun Yat-sen University）题目：Convergent Behaviors of Trefftz Method on Laplace BVPs with Singularities时间：2011年7月14日，星期四下午3：30—4：30地点：数学系致远楼102欢迎各位参加

报告人：Prof. Lee Tsung-Lin（National Sun Yat-sen University）题目：TBA时间：2011年7月14日，星期四下午4：30—5：30地点：数学系致远楼102欢迎各位参加

题 目：Approximation Properties for Group C*-algebras报告人：阮忠进教授University of Illinois, USA浙江大学求是特聘教授时 间：7月17日9:00-10:00, Part I10:30-11:30, Part II地 点：致远楼102欢迎广大师生参加！