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Course 2011-2012 a.y.

20235 - STOCHASTIC CALCULUS WITH APPLICATIONS TO FINANCE AND ECONOMICS


CLMG - M - IM - MM - AFC - CLAPI - CLEFIN-FINANCE - CLELI - ACME - DES-ESS - EMIT
Department of Decision Sciences

Course taught in English


Go to class group/s: 31

CLMG (6 credits - I sem. - OP  |  SECS-S/01) - M (6 credits - I sem. - OP  |  SECS-S/01) - IM (6 credits - I sem. - OP  |  SECS-S/01) - MM (6 credits - I sem. - OP  |  SECS-S/01) - AFC (6 credits - I sem. - OP  |  SECS-S/01) - CLAPI (6 credits - I sem. - OP  |  SECS-S/01) - CLEFIN-FINANCE (6 credits - I sem. - OP  |  SECS-S/01) - CLELI (6 credits - I sem. - OP  |  SECS-S/01) - ACME (6 credits - I sem. - OP  |  SECS-S/01) - DES-ESS (6 credits - I sem. - OP  |  SECS-S/01) - EMIT (6 credits - I sem. - OP  |  SECS-S/01)
Course Director:
DONATO MICHELE CIFARELLI

Classes: 31 (I sem.)
Instructors:
Class 31: DONATO MICHELE CIFARELLI


Course Objectives

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.


Course Content Summary
  • 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.

Detailed Description of Assessment Methods
Assessment is based on an oral exam.

Textbooks
  • 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
Last change 30/03/2011 12:00