15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Montag, 17. September 2001, 11.45-12.45, Audimax der Universität Wien


Model error and market completeness in the trading of financial derivatives

Mark Davis, Imperial College, London


It is an apparent paradox of mathematical finance that successful trading can be done on the basis of the Black-Scholes model when a basic assumption of that model - that asset price log-returns are normally distributed - is empirically false. Further, attempts at elaborating the Black-Scholes model towards greater realism often lead to incomplete market models in which hedging is theoretically impossible. In this lecture we will discuss what is required of a model to permit effective hedging, and how, by including derivative securities as independent traded assets, we can extend the simple models without losing market completeness.
This leads to some interesting inverse problems for parabolic PDEs.

E-Mail: mark.davis@ic.ac.uk
Homepage: www.ma.ic.ac.uk/~mdavis

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