20235 - STOCHASTIC CALCULUS WITH APPLICATIONS TO FINANCE AND ECONOMICS
CLMG - M - IM - MM - AFC - CLAPI - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT
Course taught in English
Go to class group/s: 31
The course is designed to provide students with the basic tools of stochastic calculus. By end of the course, students are able to handle the tools that are necessary to understand the wide range of applications in finance and economics.
In the first part, the course provides a recapitulation of the main concepts of probability. In particular, the concept of random process is clarified with simple examples. The main content of the course is then related to the definition of stochastic differential, stochastic differential equations and their applications to price options (Black and Scholes), to interest rate theory (Vasicek) and to other fields.
A survey of probability (random functions)
Brownian Motion and Ito integral
Stochastic differential and Ito formula
Stochastic differential equations; properties of solutions
Various representation formulas for the expectation of random quantities
Applications to option pricing, interest rates, perpetuities, etc.
- B. OKSENDAL, Stochastic Differential Equations. An Introduction with Applications, Berlin/New York, Springer 2006.
- D.M. CIFARELLI, L. PECCATI, Equazioni differenziali stocastiche con applicazioni economiche e finanziarie, Milano, Egea, 1998