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Financial Mathematics


Unit 1.  Basic Models of Financial Markets: One-Period Finite State Model, Securities and Their payoffs, Securities as Vectors, Operations on Securities 

  1. The Matrix as a Collection of Securities 
  2. Matrix Multiplication and portfolios 
  3. Systems of Equations and Hedging
  4. Linear Independent and Redundant Securities 
  5. The Structure of the Marketed Subspace 
  6. The Identity Matrix and Arrow-Debreu Securities 
  7. Complete Market Hedging Formula  

Unit 2.  Arbitrage and Pricing in the One-Period Model 

Unit 3.  Pricing in Dynamically Complete Markets   

Unit 4.  Towards Continuous Time     

Unit 5. Brownian motion and Ito Formulae 

Unit 6. Black-Scholes Formula