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Embedding Laws in Diffusions by Functions of Time

Fri 26 April 2013, 14:30

Alexander Cox
Bath

Probability and Statistics

Organisers: Nick Whiteley, Feng Yu

ABSTRACT
We present a constructive probabilistic proof of the fact that if B is standard Brownian motion started at 0 and mu is a given probability measure without an atom at 0 then there exists a unique left-continuous increasing function b and a unique left-continuous decreasing function c such that B stopped at the first time the process goes above b or below c has law mu. We also show that this stopping time minimises the truncated expectation among all stopping times which embed mu into B.

If time permits, I may explain why this embedding is important for the model-independent pricing of financial options on variance. (Joint work with Goran Peskir)