Bounded Rationality (Posts about measure theory)http://bjlkeng.github.io/enSun, 18 Sep 2022 02:08:36 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rssAn Introduction to Stochastic Calculushttp://bjlkeng.github.io/posts/an-introduction-to-stochastic-calculus/Brian Keng<div><p>Through a couple of different avenues I wandered, yet again, down a rabbit hole
leading to the topic of this post. The first avenue was through my main focus
on a particular machine learning topic that utilized some concepts from
physics, which naturally led me to stochastic calculus. The second avenue was
through some projects at work in the quantitative finance space, which is one
of the main applications of stochastic calculus. Naively, I thought I could
write a brief post on it that would satisfy my curiosity -- that didn't work
out at all! The result is this extra long post.</p>
<p>This post is about stochastic calculus, an extension of regular calculus to
stochastic processes. It's not immediately obvious
but the rigour needed to properly understand some of the key ideas requires
going back to the measure theoretic definition of probability theory, so
that's where I start in the background. From there I quickly move on to
stochastic processes, the Wiener process, a particular flavour of stochastic
calculus called Itô calculus, and finally end with a couple of applications.
As usual, I try to include a mix of intuition, rigour where it helps intuition,
and some simple examples. It's a deep and wide topic so I hope you enjoy my
digest of it.</p>
<p><a href="http://bjlkeng.github.io/posts/an-introduction-to-stochastic-calculus/">Read more…</a> (72 min remaining to read)</p></div>Black-Scholes-MertonBrownian motionLangevinmathjaxmeasure theoryprobabilitysigma algebrastochastic calculusWeiner processwhite noisehttp://bjlkeng.github.io/posts/an-introduction-to-stochastic-calculus/Mon, 12 Sep 2022 01:05:55 GMT