This lecture will be held at the ROM. Please see below. We review some recent developments in Probability which are motivated by problems of hedging derivatives in incomplete financial markets. This will include new variants of decomposition theorems for semimartingales, the construction of efficient hedges which minimize the shortfall risk under some cost constraint, and some results on Brownian motion related to the heterogeneity of information among financial agents.

*ROM Theatre is at 100 Queen's Park, Toronto. This lecture will be held during the Probability in Finance Workshop.