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  • Mathematics
    • Elementary Calculus
    • Linear Algebra
    • Real Analysis
    • Topology
    • Topological Vector Spaces
    • Set-Valued Analysis
    • Stochastic Analysis
    • Nonlinear Analysis
      • Fuzzy Metric Spaces
      • Probabilistic Metric Spaces
      • Fixed-Point Theory
    • Near Vector Spaces
  • Applied Mathematics
    • Probability and Statistics
      • Probability
      • Statistics
      • Applied Probability
      • Applied Statistics
    • Operations Research
      • Introduction to Operations Research
      • Systems Reliability
      • Scheduling Problems
      • Meta Heuristics
    • Optimization
      • Nonlinear Programming
      • Optimization in Vector Spaces
      • Continuous-Time Optimization
      • Robust Optimization
      • Interval Optimization
      • Fuzzy Optimization
      • Stochastic Optimization
    • Game Theory
    • Mathematical Economics
    • Mathematical Finance
    • Actuarial Mathematics
    • Foundations of Fuzzy Sets
    • Theory of Fuzzy Sets
  • Arithmetics
    • 中學算術
    • 精算數學
    • 期貨與選擇權
  • Academic Achievements
    • Academic Services
    • Published Books
    • Published Papers
    • World’s Top 2% Scientists
    • 全球前 2% 頂尖科學家
  • References
    • Whole Lists
    • Theory of Fuzzy Sets
    • Fuzziness and Randomness
    • Optimization
    • Fuzzy Optimization
    • Nonlinear Analysis
    • Game Theory
    • Mathematical Economics
    • Computational Intelligence
    • Evolutionary Computation
    • Scheduling Problems
    • Systems Reliability
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  • Hyperlink
Knowledge of Mathematics

Detailed proofs will be provided as clear as possible

  • Mathematics
    • Elementary Calculus
    • Linear Algebra
    • Real Analysis
    • Topology
    • Topological Vector Spaces
    • Set-Valued Analysis
    • Stochastic Analysis
    • Nonlinear Analysis
      • Fuzzy Metric Spaces
      • Probabilistic Metric Spaces
      • Fixed-Point Theory
    • Near Vector Spaces
  • Applied Mathematics
    • Probability and Statistics
      • Probability
      • Statistics
      • Applied Probability
      • Applied Statistics
    • Operations Research
      • Introduction to Operations Research
      • Systems Reliability
      • Scheduling Problems
      • Meta Heuristics
    • Optimization
      • Nonlinear Programming
      • Optimization in Vector Spaces
      • Continuous-Time Optimization
      • Robust Optimization
      • Interval Optimization
      • Fuzzy Optimization
      • Stochastic Optimization
    • Game Theory
    • Mathematical Economics
    • Mathematical Finance
    • Actuarial Mathematics
    • Foundations of Fuzzy Sets
    • Theory of Fuzzy Sets
  • Arithmetics
    • 中學算術
    • 精算數學
    • 期貨與選擇權
  • Academic Achievements
    • Academic Services
    • Published Books
    • Published Papers
    • World’s Top 2% Scientists
    • 全球前 2% 頂尖科學家
  • References
    • Whole Lists
    • Theory of Fuzzy Sets
    • Fuzziness and Randomness
    • Optimization
    • Fuzzy Optimization
    • Nonlinear Analysis
    • Game Theory
    • Mathematical Economics
    • Computational Intelligence
    • Evolutionary Computation
    • Scheduling Problems
    • Systems Reliability
  • Arts
    • Classical Musics
    • Paintings
    • Sculptures
  • Hyperlink
Knowledge of Mathematics

Detailed proofs will be provided as clear as possible

Mathematical Finance

Introduction to Financial Derivatives

  • Financial Derivatives 
  • Call and Put Spot Options
  • Futures Call and Put Options
  • Forward Contracts

Mathematical Finance in Discrete Time

  • Finite Spot Markets
  • Finite Futures Market
  • Futures Prices Versus Forward Prices
  • The Cox-Ross-Rubinstein Model

Market Imperfections

  • Perfect Hedging
  • Mean-Variance Hedging

The Black-Scholes Model

  • Spot Market
  • Riskless Portfolio Method
  • Sensitivity Analysis
  • Futures Market
  • Option on a Dividend-Paying Stock
  • Stock Price Volatility

Foreign Market Derivatives

  • Currency Markets
  • Cross-Currency Market Model
  • Currency Forward Contracts and Options
  • Foreign Equity Forward Contracts
  • Foreign Market Futures Contracts
  • Foreign Equity Options

American Options

  • Valuation of American Claims
  • American Call and Put Options
  • Early Exercise Representation of an American Put
  • Analytical Approach
  • Option on a Dividend-Paying Stock

Exotic Options

  • Package Options
  • Forward-start Options
  • Chooser Options
  • Compound Options
  • Digital Options
  • Barrier Options
  • Lookback Options
  • Asian Options
  • Basket Options

Mathematical Finance in Continuous Time

  • Standard Market Models
  • Multidimensional Black-Scholes Model
  • The Greeks
  • Approximations of Continuous Time Market Models
  • Futures Markets

Fixed-Income Market

  • Interest Rates and Related Contracts
  • Bond Market
  • Models of the Short-Term Rate
  • Models of Instantaneous Forward Rates
  • Models of Bond Prices and LIBOR Rates
  • Option Valuation in Gaussian Models

Bibliography

 

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