Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29

Tung Hai University Chiao Tung UniversityTaiwan University Tsing Hwa University

National Integrated Projecton Fundamental Mathematics

2001~ 2005

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 22

Fundamental Mathematics

Workstation and Teaching Lab Workstation and Teaching Lab

FinanceBiology

Scientific Computati

on

http://www.math.thu.edu.tw/~finbiosci

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 33

Mathematics Finance Chiao-TungChiao-Tung University University : : Prof. Yuah-Chung Sheu Prof. Yuah-Chung Sheu

Quantitative Finance

TaiwanTaiwan University : Prof. I-Liang Chen University : Prof. I-Liang Chen

Mathematics Finance

Tunghai Tunghai University : Prof. Fang-Bo YehUniversity : Prof. Fang-Bo Yeh

Mathematics Finance

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 44

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 55

Financial Engineering

By using financial instruments : forwards, f forwards, futures, swaps, options, and related productsutures, swaps, options, and related products

To restructure or rearrange cash flows

To achieve particular financial goals particul particularly the management of financial risk.arly the management of financial risk.

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 66

Mathematics Tool

Analytical ToolAnalytical ToolFinancial EconomicsFinancial EconomicsStochastic AnalysisStochastic AnalysisOptimal Control TheoryOptimal Control TheoryFunction Analytic TheoryFunction Analytic TheoryPartial Differential Equation Partial Differential Equation

Computation ToolComputation ToolNumerical and SimulationNumerical and Simulation

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 77

Control Engineering

Standard Control SystemStandard Control System

G

K

w z

yu

G : Finance System : Internal UncertaintiesK : 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 88

H-infinity Modeling

3WG

K

n

d

r

1W

2W

1z

2z

3z

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 99

Financial Market Modeling

Modeling Modeling GG and and :: Deterministic ModelingDeterministic Modeling

H-infinity MethodH-infinity MethodShaping MethodShaping Method

Stochastic Modeling Stochastic Modeling FilteringFilteringSystem Identification: on-line,System Identification: on-line, off-lineoff-line

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 1111

Observed basedObserved basedControllerController

Management of Financial Risk

StabilizableStabilizableDetectableDetectable

Controller Controller KK

Dynamic HedgingDynamic HedgingStrategyStrategy

HedgeableHedgeableAttainableAttainable

Management of Management of Financial RiskFinancial Risk

Control Engineering Financial Engineering

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 1212

Problems in Finance

Study ofStudy of Arbitrage, Hedging, PricingArbitrage, Hedging, PricingConsumption/Investment OptimizationConsumption/Investment OptimizationIncomplete and/or Constrained MarketsIncomplete and/or Constrained MarketsEquilibrium 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.29 1313

Thank You.

Fang-Bo Yeh, Dept. of Mathematics, Tunghai Univ.

2004.Jun.29 1414