Research by T. Zamrik
Welcome. This is where I keep my research: working papers on stochastic analysis, control and mean field games; Jupyter notebooks that work a question through in code, to download or to run on Kaggle; and a blog that takes a question from the world and works it through to the mathematics, with data and models you can run in the browser. The newest of each is just below. — T. Zamrik
37 papers since 2022 · 4 notebooks · 69 blog posts · 6 research areas
Latest
New papers
Littlewood’s Rule for a Home Battery
How to run a home battery on Ontario's Ultra-Low Overnight plan with Littlewood's rule, what it saves on real bills, and when installing one pays.
Queue-Reactive Dynamics on the Full Order-Book Profile
Queue-reactive models of the limit order book make order arrival and cancellation rates functions of the current queue size, and reproduce the mean…
Skew Brownian Motion: One Biased Site and the Asymmetry It Buys
Skew Brownian motion is ordinary Brownian motion everywhere except one point: at the origin each excursion chooses the positive side with probability α…
New notebooks
The Bold Play That Passes the Funded Challenge
A runnable notebook: a $50K funded-account evaluation replayed on three years of Nasdaq futures, with the trailing-drawdown maths and bold play.
The Cellar That Is Warmest in Winter
A runnable notebook: Fourier's yearly temperature wave in the ground, solved by Crank–Nicolson, reversed at 7 m, and read back from two thermometers.
The Noise That Looks Like Correlation
A runnable notebook: the Marchenko–Pastur law separates noise from structure in a correlation matrix, and cleaning it fixes a portfolio's promised risk.
From the Blog
The Shock That Refuses to Break
A weak tidal bore arrives as a train of waves whose first wave is twice the step. The KdV equation, solved, with a live board for any river.
The Rule That Fits One Ward
At 85% occupancy a 100-bed ward is full about once a month, a 20-bed ward within a week, a 500-bed hospital every six years. The OU first-passage maths.
The Barrier That Comes Early
A price at $100 takes nine years on average to reach $120, yet has a 40% chance within a year. The GBM hitting-time formula and up-and-out options.
All 37 papers →All 4 notebooks →All 69 essays →
Research interests
I work on stochastic analysis and optimal control, and on what happens when many decision-makers optimise at once: mean field games, market models and mathematical finance. A typical paper starts from a practical question, when to act and how hard, and ends with an equation solved as explicitly as it allows and checked numerically.
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Reading and citing
Most papers, and all of the notebooks and the blog, are free to read; a few papers are restricted. Every paper carries its own serial number, printed on the paper and in its address, so a citation always points at one document (how to cite). Where a paper’s code is published, it is on GitHub, at github.com/Dr-Zamrik, so its numbers can be re-run rather than taken on trust.
Each notebook is a Jupyter notebook you can download as an .ipynb or run on Kaggle, where its numbers are checked against the page before it carries its Kaggle button.
The blog starts from a story and ends in the mathematics, with data, code and live models; some essays grow into papers.
