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## National Integrated Project on Fundamental Mathematics

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**National Integrated Projecton Fundamental Mathematics**2001~ 2005 Tung Hai University Chiao Tung University Taiwan University Tsing Hwa University**Finance**Biology Scientific Computation Fundamental Mathematics • Workstation and Teaching Lab http://www.math.thu.edu.tw/~finbiosci**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**Workshops**• Financial Engineering Theory and Design (I) 2004 Feb. 12, 13 Sun Moon Lake • Financial Engineering Theory and Design (II) 2004 June 29,30~July 1 Tunghai Campus • Mathematics Finance 2004~2005**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.**Mathematics Tool**• Analytical Tool • Financial Economics • Stochastic Analysis • Optimal Control Theory • Function Analytic Theory • Partial Differential Equation • Computation Tool • Numerical and Simulation**Control Engineering**• Standard Control System G : Finance System : Internal Uncertainties K : Reconstruct Rearrange w z G w : External Uncertainties z : Financial Risk u : Control Strategy y : Financial Tools y u K**d**r G n K H-infinity Modeling**Financial Market Modeling**• Modeling G and : • Deterministic Modeling • H-infinity Method • Shaping Method • Stochastic Modeling • Filtering • System Identification: on-line,off-line**Management of Financial Risk**Financial Engineering Control Engineering Management of Financial Risk Controller K Hedgeable Attainable Stabilizable Detectable Dynamic Hedging Strategy Observed based Controller**Problems in Finance**• Study of • Arbitrage, Hedging, Pricing • Consumption/Investment Optimization • Incomplete and/or Constrained Markets • Equilibrium • Differential Information, • Term-Structure of Interest Rates, • Transaction Costs, Credit Risk, etc.