I ended my short visit to the UK by giving a talk on stock loans at the Nomura Seminar Series in Oxford yesterday.

There could not be a better place for me to present about this particular paper. It extends previous results by Xunyu Zhou to incomplete markets, using techniques developed by Vicky Henderson and Thaleia Zariphopoulou, all three of them members of the impressive Oxford-Man Institute. Alas, by a series of unfortunate events, they were all out of the country and could not attend my talk, but I maintain that the place was ideal, if only because it gave me the chance to take pictures of some Harry Potter locations.

## Saturday, October 30, 2010

## Thursday, October 28, 2010

### Chaos at Imperial College

No, no, I don't mean that they run a particularly disorganized college.

It is just that I presented the most recent version of my work on calibration of chaotic models for interest rates there yesterday. The slides for the talk can be found here, but I have not figured out a way to upload the movies to my website in a concise manner yet, so if you are interested you can write me an e-mail.

As I mentioned in the talk, presenting about chaotic models at Imperial College is a bit like giving a talk at the Sistine Chapel on recent advances in fresco technique. Most of the fundamental work on axiomatic positive interest rates was done by Lane Hughston and his collaborators, so it was a real treat to show them my modest contribution to the subject.

Many new and old friends were in attendance, including my phd supervisor Ray Streater, as well as my recent phd student Tsunehiro Tsujimoto, but somehow I missed the opportunity to register this tri-generation encounter with a picture.

## Sunday, October 24, 2010

### Games and options at Paris Nord

So there is irrefutable evidence that the number of reader of this blog is strictly larger than zero: Jean-Michel Courtault told me he got wind that I was spending time in Paris through a colleague who follows the blog and invited yours truly to give a talk at Universite Paris Nord.

I use the opportunity to brush up on some old work I did on real options and game theory. The intersection between the two approaches is actually quite tricky, especially in incomplete markets. But I'm getting close to completing two papers on the topic - one in discrete, the other in continuous time - and will post them when they are ready. In the mean time, the slides for the talk can be found here.

I use the opportunity to brush up on some old work I did on real options and game theory. The intersection between the two approaches is actually quite tricky, especially in incomplete markets. But I'm getting close to completing two papers on the topic - one in discrete, the other in continuous time - and will post them when they are ready. In the mean time, the slides for the talk can be found here.

## Saturday, October 23, 2010

### Bubbles course

As part of my sabbatical duties here in Paris, I agreed to give a graduate course on asset price bubbles.

The course started on October 15th, and in the first lecture I discussed the theory of "rational bubbles", that is to say, bubbles that can arise in a well defined rational expectations model, simply for being a possible solution of the corresponding homogeneous Euler equation (apart from the usual "fundamental value" term, which is a particular solution associated with the inhomogenous equation with dividends).

The catch is that the expected value of such rational bubbles must grow exponentially, so they are typically ruled out by some "transversality" condition (such as constraints in the total wealth in the economy). Nevertheless, they are a good place to start studying bubbles, if only because the "irrational" ones are much more difficult to characterize.

I'll be using this page to post references for the course as it progresses. Eventually there might be slides or even notes available, but don't create any expectation (rational or otherwise) about them.

The course started on October 15th, and in the first lecture I discussed the theory of "rational bubbles", that is to say, bubbles that can arise in a well defined rational expectations model, simply for being a possible solution of the corresponding homogeneous Euler equation (apart from the usual "fundamental value" term, which is a particular solution associated with the inhomogenous equation with dividends).

The catch is that the expected value of such rational bubbles must grow exponentially, so they are typically ruled out by some "transversality" condition (such as constraints in the total wealth in the economy). Nevertheless, they are a good place to start studying bubbles, if only because the "irrational" ones are much more difficult to characterize.

I'll be using this page to post references for the course as it progresses. Eventually there might be slides or even notes available, but don't create any expectation (rational or otherwise) about them.

## Tuesday, October 19, 2010

### Mathematical finance at the old Paris Bourse

It turns out that most things related to mathematical finance in Paris are named after Louis Bachelier. Apart form the Bachelier seminars that I mentioned in this post, there is also the Institute Louis Bachelier, a high level research center house at the Palais Brongniart, the original quarters for the Bourse de Paris.

The name and location couldn't be more perfect, given that Bachelier is the undisputed founder of mathematical finance and used the Bourse as a practical example for his

In any case, I went there yesterday for two back-to-back talks (no link available). The first was by Lorenzo Bergomi, who spoke about issues related to estimating asset volatility and correlation in asynchronous markets and the second was by Emannuel Gobet, who gave a comprehensive overview of expansion techniques for calculating expectations (e.g option prices) with several examples drawn from popular models for stock prices.

The name and location couldn't be more perfect, given that Bachelier is the undisputed founder of mathematical finance and used the Bourse as a practical example for his

*Theorie de la Speculation.*

In any case, I went there yesterday for two back-to-back talks (no link available). The first was by Lorenzo Bergomi, who spoke about issues related to estimating asset volatility and correlation in asynchronous markets and the second was by Emannuel Gobet, who gave a comprehensive overview of expansion techniques for calculating expectations (e.g option prices) with several examples drawn from popular models for stock prices.

## Wednesday, October 13, 2010

### The Theory of Interstellar Trade

When I switched from physics to finance one of the first things I was told was that economics papers have an abnormally long review process. It is said that the CIR paper, for example, was in circulation 5 years before it was finally published.

But this Krugman paper clearly holds the record: it was written when he was a young assistant professor in 1978 and has just appeared in

Besides combining two of my passions, the paper is pricelessly funny. Favorite quote so far: "the reader must, of course, be careful not to confuse relative generality with general relativity".

I'll read it carefully and try to come up with a follow up taking into account what happened in financial markets in the last 32 years !

But this Krugman paper clearly holds the record: it was written when he was a young assistant professor in 1978 and has just appeared in

*Economic Inquiry*this month.Besides combining two of my passions, the paper is pricelessly funny. Favorite quote so far: "the reader must, of course, be careful not to confuse relative generality with general relativity".

I'll read it carefully and try to come up with a follow up taking into account what happened in financial markets in the last 32 years !

## Monday, October 11, 2010

### Steven Shreve in Paris

Steve gave a talk at Ecole Polytechnique today describing a model for the optimal way to purchase a large number of shares of an asset against a limit-order sell book of arbitrary shape. This generalizes the recent but already well--known work of Obizhaeva and Wang using clever stochastic analysis arguments.

If you missed his talk today you can still watch it tomorrow at the Petits Déjeuners de la Finance.

After that he will be en route to London where he is going to deliver one of his trademark courses on stochastic calculus. Everyone who has ever attended one of his talks knows why banking types pay big money for his lectures.

If you missed his talk today you can still watch it tomorrow at the Petits Déjeuners de la Finance.

After that he will be en route to London where he is going to deliver one of his trademark courses on stochastic calculus. Everyone who has ever attended one of his talks knows why banking types pay big money for his lectures.

## Saturday, October 9, 2010

### Seminaire Bachelier

The different math finance research groups in Paris (from Ecole Polytechnique, Université Paris Dauphine, CREST, Universite de Paris VI- VII, Université d'Evry, and Université de Marne La Vallée) jointly organize a series of seminars at the Institute Henry Poincare, at the heart of the Latin Quarter.

For visitors like me, it is a wonderful opportunity to meet students and researchers from all over Paris under the same roof.

Once a year, they dedicate an entire day to talks by PhD students, in many cases giving them the first chance to present their work in front of a friendly but rigorous audience.

I spent the day yesterday attending one of these

For visitors like me, it is a wonderful opportunity to meet students and researchers from all over Paris under the same roof.

Once a year, they dedicate an entire day to talks by PhD students, in many cases giving them the first chance to present their work in front of a friendly but rigorous audience.

I spent the day yesterday attending one of these

*journee des doctorants*and was immensely impressed by the quality of the talks and the results presented. It also forced me to step up my french.
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