Portale di Ateneo - En.Unibs.it

- Stochastic processes
- Martingales
- Brownian motion and related processes (Brownian motion with drift, geometric Brownian motion, Brownian bridge)
- Riemann and Stieltjes (deterministic) integrals: definition and properties
- Overview of ordinary differential equations
- Ito (stochastic) integrals: definition and properties
- Ito's lemma: "stochastic differential" and (deterministic) differential of a function
- Stochastic differential equations: introduction, analitic and numerical solution methods of simple cases
- Changes of probabilities: from random variables (change of the mean) to stochastic processes (change of the drift through the Girsanov theorem and the Radon-Nikodym derivative)
- Pricing of derivatives with Partial Derivative Equations (replicating portfolio) and with equivalent martingale measures (absence of arbitrage opportunities)
- Monte Carlo method for the pricing of derivatives when an analitic solution is unfeasible
- Pricing of derivatives through approximation with discrete time discrete state stochastic processes (i.e. binomial process)
- Markov chains: definition, classification of the states, stationary distribution for ergodic chains
- Application of Markov chains with finite states: credit risk valuation