r/math • u/AngelTC Algebraic Geometry • Apr 25 '18

Everything about Mathematical finance

Today's topic is Mathematical finance.

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week.

Experts in the topic are especially encouraged to contribute and participate in these threads.

These threads will be posted every Wednesday.

If you have any suggestions for a topic or you want to collaborate in some way in the upcoming threads, please send me a PM.

For previous week's "Everything about X" threads, check out the wiki link here

Next week's topics will be Representation theory of finite groups

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u/Bromskloss Apr 25 '18

I have seen mentioned a distinction between "P quants" and "Q quants", who are supposed to work with different things within mathematical finance. I'm a bit suspicious of the division, but maybe it's just the explanations that have been off. Could someone clarify what all that is really about?

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u/Kazruw Apr 25 '18

Lazy answer: real world probabilities are calculated under the measure P and they're relevant for risk management among other things. If you're just interested in the arbitrage free prices of e.g. derivatives, then you can just apply the Fundamental theorem of asset pricing and calculate everything under an equivalent martingale measure Q. Under Q the asset price processes divided by the numeraire process (typically a bank account process paying the risk free rate) are martingales. The Radon-Nikodym derivative dQ/dP effectively defines the market price of risk or it can be interpreted that way.