Friday, April 23, 2010

The Frittelli lectures

Marco Frittelli was here this week and gave two guest lectures in my graduate course. In his first lecture he reviewed the theory of risk measures, with particular emphasis on their representation in terms of the bi-conjugate functional given by the Fenchel-Moreau theorem. This leads naturally to the study of dual systems (other than the classical setting with bounded random variables and their dual set "ba"), and in particular Orlicz spaces. From there it was just a small leap into Banach lattices and the study of order continuous functionals. In the end it all came back to risk measures, for example by showing the the Fatou property is nothing but continuity below, etc.

The focus of his second lecture was utility maximization, where he showed that allowing for generally unbounded price processes and contingent claims naturally leads again to Orlicz spaces, in the sense that admissible portfolios have losses controlled by random variables that are compatible with the given utility function, and therefore belong to a specific Orlicz space associated with it. From there it doesn't take long to realize that the indifference price of a claim gives rise to a risk measure on an Orlicz space.

In short, the two lectures were a prime example of elegance and internal consistency, and a great way to conclude the graduate course. Apart from that, Marco also discovered the best cappuccino in Toronto. But since this information is valuable, you have to contact me personally to obtain it :)

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