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.