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Multiscale modeling, asymptotic analysis, and their applications in finance (I,II)
Prof. Chuan-Hsiang Han ( Department of Quantitative Finance, National Tsing Hua University )

2008 - 03 - 14 (Fri.)
10:20 - 12:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

During the last two decades, financial mathematics has emerging as an active branch in applied mathematics. Problems arising from modern finance are often resolved from applications of various techniques including probability and statistics, differential equations, optimization and control theory, scientific computations, etc. In this talk, the evaluation of financial derivatives under an incomplete market is treated by two approaches. First, multiscale modeling in volatility processes is shown to be powerful for calibration to the term structure of implied volatility surface. In mathematical terms, an inverse problem is solved from asymptotics of a PDE by means of singular and regular perturbations. Second, we consider the usage of Monte Carlo and Quasi Monte Carlo simulations to solve high dimensional PDEs. A variance reduction method, namely the martingale control variate method is proposed to improve the convergent speed. The martingale control comprises of a low dimensional PDE obtained from the homogenization of multiple time scales. This method turns out to be general enough to solve for variational inequalities. In financial terms, a delta hedging portfolio is effective to reduce the risk of a financial derivative. In the end, some challenging problems are discussed.

Time:March 7, 2008 - January 31, 2009
Room:
Organizer:I-Liang Chern ( Department of Mathematics, National Taiwan University )

Available Talk List

2008-03-07 (Fri.)		Causality of Wave Propagation (I)
2008-03-14 (Fri.)		Multiscale modeling, asymptotic analysis, and their applications in finance (I,II)
2008-04-11 (Fri.)		Average performance of the sparsest approximation using a dictionary
2008-04-25 (Fri.)		Anomalous Dispersion and Superluminal Propagation
2008-05-09 (Fri.)		Imaging of Multiple Targets in Rician/Rayleigh Fading Media
2008-05-09 (Fri.)		What are networks？
2008-05-16 (Fri.)		Some Effective Properties of the Periodic Structure: a Homogenization Theory Study
2008-05-23 (Fri.)		生物運動力學的若干研究
2008-09-26 (Fri.)		Introduction to Homogenization Theory I, II
2008-10-03 (Fri.)		Two-Scale Convergence and Homogenization of Periodic Structures
2008-10-17 (Fri.)		Homogenization Theory for the Elasticity I, II
2008-10-31 (Fri.)		Memory Effects and Homogenization
2008-11-14 (Fri.)		Maxmizing Band Gaps in 2-D Photonic Crystals
2008-11-21 (Fri.)		What is weak convergence?
2008-11-27 (Thu.)		What is weak convergence?
2008-12-26 (Fri.)		Solving Guided Wave Modes in Plasmonic Crystals
2009-01-09 (Fri.)		Solving Guided Wave Modes in Plasmonic Crystals II
2009-01-16 (Fri.)		Band Gap Optimization for Photonic Crystals -Part I: Introduction
2009-02-20 (Fri.)		Investigation of Transport and Mixing in Microchannel Driven by Capillary Pumping
2009-02-27 (Fri.)		Band Gap Optimization for Photonic Crystals (Part II: Result and Discussion)
2009-03-06 (Fri.)		Analytical solution of electro-osmotic flow in a periodic structure of the filter
2009-03-13 (Fri.)		Homogenization Theory and Its Application
2009-03-20 (Fri.)		Review of achieving transparency with plasmonic and metamaterial coatings
2009-05-01 (Fri.)		Revisiting the aerodynamics of hovering flight using simple models
2009-05-22 (Fri.)		Electro-osmotic flow in a micro-channel with corrugated walls:coherence between the electric potential and the wall shape function
2012-12-05 (Wed.)		SSS