This workshop is concerned with the so called super-replication approach to price European contingent claims. It will be substantially divided in 3 parts:

1. Introduction: the arbitrage pricing of options and others contingent claims starting with a simple one dimensional model (Black and Scholes case); what happens when the volatility is unknown? The superreplication approach (which is not the only possible approach) and the bounds for the price of the contingent claim.
2. Qualitative survey on mathematical treatment of the superreplication approach: Black-Scholes-Barenblatt equations, viscosity solutions, superstrategies and substrategies (report on a recent work with T.Vargiolu). Two words on the general approach.
3. Possible applications and examples:
   • the case of two assets with unknown mutual correlation
   • the case of interest rate derivatives
   • discussion on the applicability of the hedging approach: the case of an Italian insurance company: INA.

References

• For reference on the above general arguments see e.g. Musiela & Rutkowski, Martingale methods in financial modelling, Springer, Berlin 1997.

Please feel free to bring this to the attention of interested colleagues.