Stochastic Processes and Stochastic Calculus with applications to Economics and Finance (Master class 2016)
Description
The course took place in summer 2016, in San Miniato (Pisa) as the Summer School of Mathematics for Economic and Social Sciences organized by Scuola Superiore Sant’Anna (Pisa). It was held by Maurizio Pratelli as main lecturer, with the assistance of Eni Musta and myself for additional seminars and exercise sessions. The goal was to provide a crash course in stochastic analysis to give the necessary mathematical background for the main applications in economics and finance.
Teaching material
- Slides of the lectures:
- Review of Basic Concepts in Probability
- Conditional Expectation
- Markov Chains
- Martingales
- Brownian Motion
- Stochastic Integral and Itô’s Formula
- Two Fundamental Results on Stochastic Integration
- Stochastic Differential Equations and their link with Partial Differential Equations
- Complete and Incomplete Market Models
- (Short) Introduction to Interest Rate Models
- Slides of the seminars:
- A collection of exercises
