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 · 5 notebooks · 72 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
63% of Stocks Lost to the Average Stock
A runnable notebook: 288 of 459 S&P 500 stocks (62.7%) finished five years below the average stock. Compounding and volatility drag predict 60.6%.
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.
From the Blog
Right 50.75% of the Time
Medallion was reportedly right 50.75% of the time on 150,000–300,000 trades a day. How that tiny edge becomes a fortune, and the price of leverage.
What a Stop-Loss Costs
In a random walk every stop-loss costs money. On the S&P 500 since 1990 a 5% stop cost a quarter, a 10% one broke even. And the falling knife, derived.
Should You Wait for a Dip?
Waiting for a 10% dip lost to buying at once in 72% of months since 1990. When waiting does pay: optimal entry for a price that comes back.
All 37 papers →All 5 notebooks →All 72 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.
