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
36 papers since 2022 · 1 notebook · 61 blog posts · 6 research areas
Latest
New papers
The Price of a Yaw: Optimal Deadbands and Filters for Wind-Turbine Yaw Control, Calibrated on SCADA Data
A wind turbine must keep its rotor facing a wind whose direction never stops moving, and every yaw that realigns it wears the yaw system.
Dividends When Capital Is Slow: de Finetti’s Problem with a Sticky Boundary
Dividend models give a firm at zero surplus two fates: it is ruined, or capital arrives instantly and reflects it back into business.
The Derived Time Stop
A swing trade is a hypothesis with a deadline.
New notebooks
The Jensen Gap at Grand Forks, 1997
A runnable notebook: the Weather Service's own outlook record, the 49-foot forecast, the 52-foot dikes and Jensen's gap, computed in Python.
From the Blog
The Average That Drowned a City
Grand Forks built its dikes to a 49-foot median forecast; the river crested at 54.35. Jensen's inequality and the forecaster's own record explain why.
The Cube Root That Runs the Treasury
How much cash should a firm hold? For a random cash flow and a fee per transfer, the best rule is a band whose return point is a cube root.
De Rerum Electione: The Choice That Is Not a Swerve
A verse sequel to De Rerum Stochástica: Cicero on the swerve, Laplace's demon, Born's dice, and why freedom lives in the control, not the noise.
All 36 papers →All 1 notebook →All 61 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.
Browse by area
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.
