I agree, I don’t think it is magic. But it is universal, at least in complete markets. You can get there via a martingale representation theorem or a separation of the Radon-Nikodym derivative. The aspect that is still somewhat mysterious to me is that the natural numeraire is equal to the growth op...

Wait - was he actually accused of drunkenly pinching someone? That would be too perfect!

Yes

Sorry, the volatility in the process for A should of course be [$] \lambda [$].

This is even simpler to carry out in a binomial model, but using the BSM environment and standard notation, define the risk premium as [$] \lambda = \frac{\mu - r}{\sigma} [$]. Then you can create a dynamic portfolio with a constant fraction of its value given by [$] \frac{\lambda}{\sigma} [$] inves...

I’m a little late joining this party, but one perspective that I find to be kind of useful is the notion of the natural numeraire, aka the stochastic discount factor that makes discounted prices martingales under the P measure. No need for anything or anybody to be risk neutral, and the pricing resu...

I’ve probably interviewed more quants than most of the remaining survivors around here. In the early years, I found myself asking a lot of brain teasers (Why are man hole covers round? How many windows are there in Manhattan?). I think it made me feel clever, but that was about it. Then I drifted in...

Travelling to Poland in the festive season is not the most relaxing experience, especially now when they havent yet hired back the staff after the corona lockdown. But Kraków is quite nice in the winter, and close to beautiful mountains - you can visit Zakopane. Prepare some warm clothes though. I ...

I didn’t mean that to sound like a piece of marketing speech, but I don’t think that it is a coincidence that a key driver of this development was Simon Peyton Jones.

I like it, a lot! It basically extends the functional programming paradigm that is a foundational concept of the original spreadsheet design to a wide range of real world applications.

Sorry - I missed this the other day (it’s been a rough week). I sat next to him on a bus ride at a conference years ago, and he was the sort of guy that you will remember having sat next to! RIP

Given that the cheapest and least inconvenient method of abortion is performed with medication, there is no prize for guessing that the primary provider in half the country will be Mexican gangs. They already have the logistics and distribution network. You thought the war on drugs was ugly? Wait un...

Well, “fuck Elon” is always a good start. But the victims of the evangelical Republicans are mostly neither Democrats not Republicans. They are just people. Mostly women and girls, whose bodies they will no longer have much say over, but there are obviously men and boys with an interest in the matte...

It is truly shocking to me that a country as violent and replete with weapons as the US has not seen much in the way of political/judicial (to the extent you can make a distinction) assassinations during the last few decades. I predict that will change rapidly. Probably not to the level of Mexico, b...

We can hope that a number (well, six to be precise) Supreme Court justices retire or otherwise become unable to fulfill their duties over the next few days, and can thus be promptly replaced by a clean slate that can start overturning precedent rulings, starting with today’s. Clarence Thomas has alr...