Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ. 2004.Jun.29 Tung Hai University Chiao Tung University Taiwan University Tsing Hwa University National.

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Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ Jun.29 Tung Hai University Chiao Tung University Taiwan University Tsing Hwa University National Integrated Project on Fundamental Mathematics 2001~ 2005

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 2 Fundamental Mathematics Workstation and Teaching Lab Workstation and Teaching Lab Finance Biology Scientific Computation

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 3 Mathematics Finance Chiao-Tung University : Prof. Yuah-Chung Sheu Chiao-Tung University : Prof. Yuah-Chung Sheu Quantitative Finance Taiwan University : Prof. I-Liang Chen Taiwan University : Prof. I-Liang Chen Mathematics Finance Tunghai University : Prof. Fang-Bo Yeh Tunghai University : Prof. Fang-Bo Yeh Mathematics Finance

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 4 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

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 5 Financial Engineering forwards, futures, swaps, options, and related products By using financial instruments : forwards, futures, swaps, options, and related products To restructure or rearrange cash flows particularly the management of financial risk. To achieve particular financial goals particularly the management of financial risk.

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 6 Mathematics Tool Analytical Tool Analytical Tool Financial Economics Financial Economics Stochastic Analysis Stochastic Analysis Optimal Control Theory Optimal Control Theory Function Analytic Theory Function Analytic Theory Partial Differential Equation Partial Differential Equation Computation Tool Computation Tool Numerical and Simulation Numerical and Simulation

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 7 Control Engineering Standard Control System Standard Control System G K w z y u G : Finance System : Internal Uncertainties K : Reconstruct Rearrange w : External Uncertainties z : Financial Risk u : Control Strategy y : Financial Tools

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 8 H-infinity Modeling G K n d r

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 9 Financial Market Modeling Modeling G and : Modeling G and : Deterministic Modeling Deterministic Modeling H-infinity Method H-infinity Method Shaping Method Shaping Method Stochastic Modeling Stochastic Modeling Filtering Filtering System Identification: on-line, off-line System Identification: on-line, off-line

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun Observed based Controllerz Management of Financial Risk StabilizableDetectable Controller K Dynamic Hedging Strategy HedgeableAttainable Management of Financial Risk

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun Observed based Controller Management of Financial Risk StabilizableDetectable Controller K Dynamic Hedging Strategy HedgeableAttainable Management of Financial Risk Control Engineering Financial Engineering

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun Problems in Finance Study of Study of Arbitrage, Hedging, Pricing Arbitrage, Hedging, Pricing Consumption/Investment Optimization Consumption/Investment Optimization Incomplete and/or Constrained Markets Incomplete and/or Constrained Markets Equilibrium Equilibrium Differential Information, Differential Information, Term-Structure of Interest Rates, Term-Structure of Interest Rates, Transaction Costs, Credit Risk, etc. Transaction Costs, Credit Risk, etc.

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun Thank You.

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.2004.Jun.29 14