Advanced Course on Mathematical Finance, Cortona 2006

Lecturers: Location: Palazzone di Cortona>, Scuola Normale Superiore, Italy
Organization: Scuola Matematica Interuniversitaria (SMI)
Web Page/Announcement:
Duration: July 24 - August 11, 2006 (three weeks)
Language: English


Part I: Stochastic Integration (Lecturer: U. Schmock)

Motivation: Let S denote a stochastic process describing the evolution of the discounted price of an asset, and let H be the process describing the (possibly random) number of these assets at any given time in the investor's portfolio. The gains and losses of this investment strategy H is given by the stochastic integral of H with respect to S. It therefore lies at the heart of modern, continuous-time mathematical finance to clarify, for which investment strategies H and price processes S this stochastic integral is mathematically well defined and what its properties are.


  1. We will follow the approach given in Ph. Protter's textbook, developing the theory of general stochastic integration with respect to semimartingales, which includes the cases of Brownian motion and Lévy processes. Applications of the theory, in particular to the modelling to the stochastic evolution of the term structure of interest rates, will be given in Prof. Runggaldier's part of the course. Ph. Protter's book contains an extensive list of exercises, which can be discussed in the problem-solving sessions.
  2. Depending on time and interest of the course participants,
  3. will be treated in the seminars. Lecture notes for preparing these seminars are available upon request.

Prerequisites: The main topic of the course requires familiarity with measure theoretic probability theory and basic results about martingales, because these will be used without proofs. The textbook by D. Williams and Chapter 2 of the textbook by S. Ethier and T. Kurtz are certainly a good source.


Part II: Term Structure of Interest Rates, Hedging (Lecturer: W. Runggaldier)

Basic Structure:

  1. Term structure of interest rates (lectures and problem-solving sessions and seminars)
  2. Hedging of general claims by martingale representation (Mainly problem-solving sessions and seminars)

Specific Structure:

  1. Term structure of interest rates Remarks: The basic theory will be presented in a Brownian framework. As the lectures on the general integration theory (Prof. Schmock) progress, also settings beyond the Brownian framework will be envisaged.
  2. Hedging: After a short basic introduction during the lectures, this will be mainly a topic for the problem-solving sessions and seminars. As for the term structure, here too we shall start from a Brownian framwork that will then be gradually generalized in line with the general integration theory.


Possible additional material for lectures and problem-solving sessions and related specific journal articles will be made available on site.


Note: For spam protection, some email addresses contain a pet after the at-sign. Please remove it manually before using the address. Secretary: Mrs Silvana Boscherini

Picture Gallery:

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