Theory of Probability and Discrete Models in Finance


We study examples of discrete models of financial markets - binomial, multi-period binomial- and, in a general framework, the two main theorems of Financial Mathematics - characterization of arbitrage-free and complete markets - and deepening the formalism of Probability theory, and stochastic processes that provide the context for this study.


  1. Fundamentals of Measure Theory and Probability
  2. Conditional Expectation
  3. Martingales
  4. Binomial Model
  5. Multi-period models
  6. Markov chains
  7. Poisson process


  • Bjork, T., An introduction to Arbitrage Theory in Continuous Time, Oxford University Press, 2004.
  • Lamberton, D. and Lapeyre, B., Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall 2008.
  • Shiryaev, A.N., Essentials of Stochastic Finance, World Scientific,