Dr. Bruno Dupire, Bloomberg and NYU.
SLIDES

Applications of the Root Solution of the Skorohod Embedding Problem in Finance

The Skorokhod embedding problem amounts to stopping a Brownian motion to hit a target density; it has interesting implications for finance: 
a) any solution leads to a model that is calibrated to the option prices of a given maturity and
b) it provides a rule to sell a (martingale) asset in order to achieve a prescribed wealth distribution. We concentrate on the Root Solution (hitting time of a barrier), which provides a canonical mapping of a density into a stopping region. We examine
1) the implications in terms of options on realized variance
2) new Monte Carlo schemes which confine the increments in both space and time at each time step