MTH 9831 Probability and Stochastic Processes for Finance I

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Instructor: Elena Kosygina

Topics:

First examples of stochastic processes and an informal introduction of basic notions and tools.

  • Random walks. Gambler’s ruin
  • Pricing by arbitrage. The binomial asset pricing model
  • Real-world and risk-neutral probabilities
  • Poisson processes

Measure-theoretic language and essential background

  • Weak convergence
  • Laws of large numbers and the central limit theorem
  • Conditional expectations
  • Martingales. Stopping times. Optional stopping theorem
  • Brownian Motion

Instructor’s Notes were distributed at each class.

Reference Books: