Research by T. Zamrik
Welcome. This is where I keep my research: working papers on stochastic analysis, control and mean field games, and a Notebook 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 · 61 notebook posts · 6 research areas
Latest
From the Notebook
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.
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.
All 61 essays →All 36 papers →
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 the whole Notebook, 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.
The Notebook starts from a story and ends in the mathematics, with data, code and live models; some essays grow into papers.
