As we reach the end of the first month in the Thematic Program, I think we are achieving most of what we wanted. The first workshop was a great excitement, followed by extended visits by several senior researchers, who gave guest lectures and talks in the subsequent weeks. The graduate courses are well under way and the postdocs and long term visitors are beginning to interact in scientifically meaningful ways.

All we have to do is keep it up for five more months without any major snafu and we can declare mission accomplished. Of course I have now jinxed myself, but we are all probabilists, not silly superstitious people, or are we ?

## Saturday, January 30, 2010

## Wednesday, January 27, 2010

### Inverse problems Tuesday

Instead of going to Fields I stayed at McMaster yesterday to host Jorge Zubelli, who gave an inverse problems tour de force in his AIMS/Phimac talk. He manage to convince us all that there is a lot to be done in the world of rigorous results for calibrating local volatility surfaces.

## Tuesday, January 26, 2010

### Quiet times at last (and a word about Bachelier)

With the first wave of visitors subsiding, we are entering a period of relative calm in the thematic program until the next major workshop at the end of March. The plan is to use this time to get to know the work done by the several postdocs in residence by making them give talks in the visitor's seminar series, which will start in full swing next Tuesday.

I certainly welcome quiet days like yesterday, when I have the chance to work on my own lectures and research problems.

In lieu of excitement, I watched Tom Hurd and Sebastian Jaimungal wrestle all day with the mountain of abstracts and papers for the Bachelier Congress. Even after the Sunday deadline had passed, submissions were still coming in, so the actual shutting down of the web interface they used (EasyChair) was a delicate stopping problem.

In the end the total number of submissions surpassed the London (2008) congress, confirming the definite increasing trend observed since the first congress in Paris (2000). Kudos for the organizing committee !

I certainly welcome quiet days like yesterday, when I have the chance to work on my own lectures and research problems.

In lieu of excitement, I watched Tom Hurd and Sebastian Jaimungal wrestle all day with the mountain of abstracts and papers for the Bachelier Congress. Even after the Sunday deadline had passed, submissions were still coming in, so the actual shutting down of the web interface they used (EasyChair) was a delicate stopping problem.

In the end the total number of submissions surpassed the London (2008) congress, confirming the definite increasing trend observed since the first congress in Paris (2000). Kudos for the organizing committee !

## Saturday, January 23, 2010

### The mystery of positive interest

Tomas Bjork concluded his three-part mini-course on Interest Rate Theory on Thursday morning with a story that is too fascinating for me not to reproduce here.

On the theme of positivity for forward rates in an HJM framework, he said that in 1996 he came across a very peculiar paper by Flesaker and Hughston titled Positive Interest. According to him, only a few times in your life you read a paper and really don't understand what is going on. Then you read more carefully, making sure that you know how the second line follows from the first, and how the third line follows from the second, and so forth until the end of the paper, thereby convincing yourself that the paper is correct, but still you really, really, don't understand what is going on. It is only during a third level of assimilation that you wake up one morning and fully understand the idea - in fact you ask yourself how could it possibly be any different.

Well, he says that as far as the Flesaker and Hughston paper goes, he is still stuck on the second level of understanding, together with most of us.

On the theme of positivity for forward rates in an HJM framework, he said that in 1996 he came across a very peculiar paper by Flesaker and Hughston titled Positive Interest. According to him, only a few times in your life you read a paper and really don't understand what is going on. Then you read more carefully, making sure that you know how the second line follows from the first, and how the third line follows from the second, and so forth until the end of the paper, thereby convincing yourself that the paper is correct, but still you really, really, don't understand what is going on. It is only during a third level of assimilation that you wake up one morning and fully understand the idea - in fact you ask yourself how could it possibly be any different.

Well, he says that as far as the Flesaker and Hughston paper goes, he is still stuck on the second level of understanding, together with most of us.

## Thursday, January 21, 2010

### Optimal growth, interest rate, and PRMIA roundtable

Eckhard Platen concluded his mini-course on the benchmark approach today, followed by a talk in the Quantitative Finance Seminar Series highlighting its applications to long dated insurance contracts. Because the optimal growth portfolio plays an essential role in the the benchmark approach, I showed Eckhard this paper by Paul Samuelson. The paper is deliciously written entirely with words of one syllable, but by dismissing the use of the log-optimal portfolio, prevented economists from undertaking serious research in this area for almost 20 years.

Tomas Bjork gave the second third of his mini-course on interest rates in the afternoon, with a detour into more advanced topics such as the Musiela parametrization and finite--dimensional realizations of HJM models. I suspect this was way over the heads of most graduate students, but thoroughly enjoyable.

At the end of the day we had a roundtable on the Incremental Risk Charge in Basel II organized by PRMIA. This was extremely well attended by local practitioners, and despite the fact that I couldn't really appreciate the regularoty nuances that poped up at times, the discussion was very entertaining.

Tomas Bjork gave the second third of his mini-course on interest rates in the afternoon, with a detour into more advanced topics such as the Musiela parametrization and finite--dimensional realizations of HJM models. I suspect this was way over the heads of most graduate students, but thoroughly enjoyable.

At the end of the day we had a roundtable on the Incremental Risk Charge in Basel II organized by PRMIA. This was extremely well attended by local practitioners, and despite the fact that I couldn't really appreciate the regularoty nuances that poped up at times, the discussion was very entertaining.

## Tuesday, January 19, 2010

### Benchmark, pancakes, and interest rates

Eckhard Platen delivered the first half of his mini-course on the Benchmark Approach today, as part of the graduate course on Foundations of Mathematical Finance. This is a fascinating topic that he and co-authors developed in the past decade or so, leading to an alternative paradigm for mathematical finance, from asset pricing to portfolio management to hedging of long-dated securities. To me, one of the most interesting results in the approach is an absolute pricing mechanism, that is, derived from the real economy as a whole, as opposed to relative pricing, in which securities in some corner of the market are priced in relation to each other. In other words, this is a healthy response to what Larry Summers famously mocked as "ketchup economics" in a piece reproduced in this post by Matthew Yglesias today.

But since we are in Canada, it is much better to talk about mapple syrup than ketchup, and the Fields Institute treated us to their delicious annual pancake lunch.

In the afternoon, Tomas Bjork delivered the first third of his mini-course on interest rate theory, which consisted of standard graduate level material, but was of course delightful to graduate students and faculty members alike, since most of us first learn financial mathematics by reading his book anyway.

But since we are in Canada, it is much better to talk about mapple syrup than ketchup, and the Fields Institute treated us to their delicious annual pancake lunch.

In the afternoon, Tomas Bjork delivered the first third of his mini-course on interest rate theory, which consisted of standard graduate level material, but was of course delightful to graduate students and faculty members alike, since most of us first learn financial mathematics by reading his book anyway.

## Saturday, January 16, 2010

### Foundations workshop comes to an end

As pointed out in a tangential comment by Rene Carmona, the organizers of the workshop reserved the last day exclusively for talks by young researchers - representatives of the next generation advancing the foundations of our subject.

At the very end of meeting, in a remark following Miklós Rásonyi's talk, Hans Follmer closed the workshop the way he had started it, by reminding us that the problems addressed by mathematical finance - bubbles included - are very much part of the real world, and that we have our work cut out for us before we can claim to have a robust understanding of financial markets.

I would like to thank all organizers, speakers and participants for a truly stimulating workshop. It was the best start I could have wished for the six months ahead of us.

At the very end of meeting, in a remark following Miklós Rásonyi's talk, Hans Follmer closed the workshop the way he had started it, by reminding us that the problems addressed by mathematical finance - bubbles included - are very much part of the real world, and that we have our work cut out for us before we can claim to have a robust understanding of financial markets.

I would like to thank all organizers, speakers and participants for a truly stimulating workshop. It was the best start I could have wished for the six months ahead of us.

## Friday, January 15, 2010

### Short and sweet

Yesterday was the shortest day of the workshop, with only three talks in the morning to allow for free time in the afternoon for interactions between participants or just plain sightseeing in Toronto.

Thaleia Zariphopoulou talked about forward utilities once more, which is just as well, because she has developed the topic so vastly that each time she presents on the subject the audience tends to learn a lot.

Michael Monoyios gave a talk on executive stock options, a subject close to my heart, and I now have many ideas for a follow-up paper extending his insider-information model to the case of a risk-averse executive.

The morning ended with Martin Schweizer explaining how the optimal wealth and the optimal portfolio arising from a utility maximization problem depend on the time horizon. The result is intuitive enough, despite the technically formidable proof, and ties well with the general theme discussed by both Thaleia and Nicole in her talks durign the workshop.

Thaleia Zariphopoulou talked about forward utilities once more, which is just as well, because she has developed the topic so vastly that each time she presents on the subject the audience tends to learn a lot.

Michael Monoyios gave a talk on executive stock options, a subject close to my heart, and I now have many ideas for a follow-up paper extending his insider-information model to the case of a risk-averse executive.

The morning ended with Martin Schweizer explaining how the optimal wealth and the optimal portfolio arising from a utility maximization problem depend on the time horizon. The result is intuitive enough, despite the technically formidable proof, and ties well with the general theme discussed by both Thaleia and Nicole in her talks durign the workshop.

## Thursday, January 14, 2010

### Equilibrium day

With the exception of Damir Filipovic and Nizar Touzi, everybody spoke about equilibrium on the third day of the workshop. What is surprising is that speakers were selected before they had to submit their talks, with the general guideline that this was going to be a workshop on foundations of mathematical finance. The fact that general equilibirum ended up being the dominat theme of the workshop shows that as a community we have moved from the arbitrage pricing to risk preferences for individual agents (risk measures, utility, indifference price etc) and are finally arriving at the task of understanding how prices are formed in markets with multiples agents, which is of course the starting point of economic theory. I for one welcome this new phase in research.

## Wednesday, January 13, 2010

### Utility functions galore

Nicole El Karoui opened the second day of the workshop with a new way to construct

Paolo Guasoni started his talk with provocative quotes from Paul Krugman and John Cochrane to motivate the study of market frictions, followed by an analysis of the fee incentives of hedge funds using utility functions for fund managers.

For the rest of the day, Semyon Malamud, Peter Bank, Kasper Larsen and Jaksa Cvitanic all talked about different aspects of markets with heterogeneous agents - one of the hottest as yet unexplored frontiers in mathematical finance.

*progressive utilitie*s using optimal wealth processes. This gives additional mathematical weight to the general theme of*dynamic*utility functions, which were popularized in the mathematical finance community through the work of Marek Musiela and Thaleia Zariphopoulou on*forward utilities*.Paolo Guasoni started his talk with provocative quotes from Paul Krugman and John Cochrane to motivate the study of market frictions, followed by an analysis of the fee incentives of hedge funds using utility functions for fund managers.

For the rest of the day, Semyon Malamud, Peter Bank, Kasper Larsen and Jaksa Cvitanic all talked about different aspects of markets with heterogeneous agents - one of the hottest as yet unexplored frontiers in mathematical finance.

## Monday, January 11, 2010

### A bang at last

We couldn't have hoped for a better start for the Foundations workshop today, with the large seminar room at full capacity, the video link to the overflow room working flawlessly, and all scheduled speakers arriving on time in Toronto.

As the first speaker, Hans Follmer set the tone for the week by delivering an impeccable talk describing the state-of-the-art in dynamic risk measures and showing, among other things, how aversion to model ambiguitiy is associated with asset bubbles. Josef Teichmann, Mihai Sirbu, XunYu Zhou and Marco Frittelli kept the level up all day, both in terms of technical dexterity and scope. By the time the reception started everybody was in good spirits and ready for the subsidized drinks.

As the first speaker, Hans Follmer set the tone for the week by delivering an impeccable talk describing the state-of-the-art in dynamic risk measures and showing, among other things, how aversion to model ambiguitiy is associated with asset bubbles. Josef Teichmann, Mihai Sirbu, XunYu Zhou and Marco Frittelli kept the level up all day, both in terms of technical dexterity and scope. By the time the reception started everybody was in good spirits and ready for the subsidized drinks.

## Sunday, January 10, 2010

### Workshop history

Because it is the weekend, I can indulge in a bit of history again. About two years ago, in January 2008, I invited Marco Frittelli to be the chair of the scientific committee for the workshop that will start tomorrow. He got to work almost immediately and used the Oberwolfach meeting that was happening that month to start inviting other people to be part of the committee, whose final composition was decided just after the Bachelier Congress in London, in August 2008. By January 2009, they had a draft list of speakers and we started sending out invitations exactly about one year ago. Most speakers accepted their invitations right away, so by February we were able to post an almost complete list of speakers on the program website. This was a big boost for us, because it conferred reality and gravitas to the whole program, making the task of organizing the other activites a lot easier. In short, we owe a lot to the folks in this scientific committee, and I plan to convey that in my opening remarks tomorrow morning.

## Friday, January 8, 2010

### Seinfeld post

This is a post about nothing, mainly because I didn't go to Fields today (lingering McMaster obligations), but also because it seems nothing really happened in our program today, except for the cancellation of Bjork's visit because Heathrow cannot handle a snow storm.

## Thursday, January 7, 2010

### On retirement income and guided tours

Quiet day for me at Fields, with not much happening related to our thematic program. The Institute itself was busy with the Short course on retirement income analytics, presented by the same triumvirate (Moshe Milevsky, Tom Salisbury and Huaxiong Huang) who will organize the Industrial-Academic Forum on Financial Engineering and Insurance Mathematics later in the program.

I spent the day updating the lecture notes for my course. We are using the Delbaen and Schachemayer book, which starts with a guided tour to the whole theory. But, since students are already finding it tough, I might have to write my own guided tour to the guided tour (with things like an introduction to the separating hyperplane theorem and the like). Of course this can lead to an infinite loop and I can quickly find myself writing about Peano's axioms, but I'll try to draw the line at something reasonable.

I have also learned how to post files on the additional site that I created for the program. Here are the papers that we discuss in the first lecture, containing the proof of the FTAP for finite probability spaces (among other things).

I spent the day updating the lecture notes for my course. We are using the Delbaen and Schachemayer book, which starts with a guided tour to the whole theory. But, since students are already finding it tough, I might have to write my own guided tour to the guided tour (with things like an introduction to the separating hyperplane theorem and the like). Of course this can lead to an infinite loop and I can quickly find myself writing about Peano's axioms, but I'll try to draw the line at something reasonable.

I have also learned how to post files on the additional site that I created for the program. Here are the papers that we discuss in the first lecture, containing the proof of the FTAP for finite probability spaces (among other things).

## Wednesday, January 6, 2010

### Graduate courses extravaganza

Now that is more like it ! Our graduate courses started today with great turnouts both in the morning (Foundations of Mathematical Finance) and afternoon (Interest rates and Credit Risk). Loads of graduate students, postdocs, faculty members and even some people from industry - exactly as it was meant to be. Hopefully we can keep up the numbers until the end of the program.

On the downside - as it appears we have to have one everyday - Tomas Bjork is stranded at Heathrow today because of a severe snow storm in England, so we had to cancel his first guest lecture originally scheduled for tomorrow morning.

On the downside - as it appears we have to have one everyday - Tomas Bjork is stranded at Heathrow today because of a severe snow storm in England, so we had to cancel his first guest lecture originally scheduled for tomorrow morning.

## Tuesday, January 5, 2010

### First day blues

Tom Hurd and I showed up at Fields today to mark the start of the thematic program for us. It was nice to settle in our offices, get personalized mugs and test the coffee machine. Spent the rest of the day dealing with admin tasks before the influx of visitors that are expected to arrive over the weekend and preparing for our respective graduate courses.

On the downside, public transport in Canada still has miles to go before they sleep... I'm looking at you TTC and your TTC Times Two with GO transit scheme that works if one travels out of Toronto and returns by the end of the day but NOT the other way around, which is what most commuters actually do.

And since this is a blog on financial math after all, let me mention the complete lack of economic incentives for buying long-term passes on the TTC: the monthly pass costs exactly one dollar more than one would spend by using two single tickets a day, five days a week. This encourages people to stack up on single tickets and use them occasionally, rather them committing to a montlhy pass that would give an incentive to leave their cars at home, which is of course the exact opposite of what an environmentally sound policy should be.

On the downside, public transport in Canada still has miles to go before they sleep... I'm looking at you TTC and your TTC Times Two with GO transit scheme that works if one travels out of Toronto and returns by the end of the day but NOT the other way around, which is what most commuters actually do.

And since this is a blog on financial math after all, let me mention the complete lack of economic incentives for buying long-term passes on the TTC: the monthly pass costs exactly one dollar more than one would spend by using two single tickets a day, five days a week. This encourages people to stack up on single tickets and use them occasionally, rather them committing to a montlhy pass that would give an incentive to leave their cars at home, which is of course the exact opposite of what an environmentally sound policy should be.

## Monday, January 4, 2010

### Modest beginnings

The thematic program officially begins today, although most of the action will start next week with the Workshop on Foundations of Mathematical Finance. Two of the graduate courses start this week, and students will have a special treat on Thursday with the guest lecture by Tomas Bjork.

I didn't go to Fields today, having spent the day sorting out a few unfinished 2009 business at McMaster, but since I resolved to post about the program everyday on this blog, I phone Alison Conway to ask what was happening.

She was slightly disappointed that not many people came to have the tea and biscuits (wait, that would have been in Cambridge) that she had prepared for the new visitors, as only two participants showed up: Kyoung-Kuk (Ken) Kim, who will be the Marsden Postodoctoral Fellow during our program, and Tom Salisbury, whom I talked about in my previous post. I guess when Tom said in his Fields newsletter article that he was "eagerly anticipating what looks to be an outstanding thematic program", he really meant it.

I didn't go to Fields today, having spent the day sorting out a few unfinished 2009 business at McMaster, but since I resolved to post about the program everyday on this blog, I phone Alison Conway to ask what was happening.

She was slightly disappointed that not many people came to have the tea and biscuits (wait, that would have been in Cambridge) that she had prepared for the new visitors, as only two participants showed up: Kyoung-Kuk (Ken) Kim, who will be the Marsden Postodoctoral Fellow during our program, and Tom Salisbury, whom I talked about in my previous post. I guess when Tom said in his Fields newsletter article that he was "eagerly anticipating what looks to be an outstanding thematic program", he really meant it.

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