1. 1 National Integrated Project on Fundamental Mathematics Tung-Hai University Chiao-Tung University Taiwan University Tsing-Hwa University 2001~ 2005

2. 2 Fundamental Mathematics Workstation and Teaching Lab. Finance Biology Scientific Computation http://www.math.thu.edu.tw/~finbiosci

3. 3 Mathematics Finance Chiao-Tung University:Prof. Yuah-Chung Sheu Quantitative Finance Taiwan University: Prof. I-Liang Chen Mathematics Finance Tunghai University: Prof. Fang-Bo Yeh Mathematics Finance

4. 4 Workshop Financial Engineering Theory and Design(I) 2004 Feb. 12, 13 Sun Moon Lake Financial Engineering Theory and Design(II) 2004 June~July Tunghai Campus Mathematics Finance 2004~2005

5. 5 Financial Engineering By using financial instruments: forwards, futures, swaps, options, and related products To restructure or rearrange cash flows To achieve particular financial goals particularly the management of financial risk.

6. 6 Mathematics Tool Analytical Tool: Financial Economics Stochastic Analysis Optimal Control Theory Function Analytic Theory Partial Differential Equation Computation Tool Numerical and Simulation

7. 7 Control Engineering Standard Control System G K wz yu G: Finance System : Internal Uncertainties K: Reconstruct Rearrange w: External Uncertainties z : Financial Risk u: Control Strategy y: Financial Tools

8. 8 Financial Market Modeling Modeling G and : Deterministic Modeling: H-infinity Method Shaping Method Stochastic Modeling: Filtering System Identification: on-line off-line

9. 9 H-infinity Modeling W1W1 W2W2 W3W3 G K z1z1 z2z2 z3z3 n d r

10. 10 Management of Financial Risk Controller K: Management of Financial Risk. Stabilizable : Hedgeable Detectable : Attainable Observed based Dynamic Hedging Controller Strategy

11. 11 Problems in Finance Study of Arbitrage Hedging Pricing Consumption/Investment Optimization Incomplete and/or Constrained Markets Equilibrium Differential Information, The Term-Structure of Interest Rates, Transaction Costs, Credit Risk, etc.