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
39 papers since 2022 · 7 notebooks · 2 tools · 76 blog posts · 6 research areas
Latest
New papers
What Does a Nonlinear Fokker–Planck Equation Buy a Mean Field Game?
Mean field games with nonlinear Fokker–Planck equations: how agents that touch change the crowd's statistics, with computed equilibria and open questions.
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…
New notebooks
Both Sides of the Policy Get Richer
A runnable notebook: Bernoulli's 1738 merchant, an 800-ruble premium on a 500-ruble risk, and why time-average growth makes buyer and insurer both richer.
Is a Lottery Ticket Ever Worth Buying?
A runnable R notebook: the roll-down rule that made a two-dollar Cash WinFall ticket worth 2.30, checked against the Inspector General's 2012 report.
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%.
New tools
Goal or Blow-Up: The Odds for a Day-Trading Account
How likely am I to reach my goal before I blow up my account, and when?
Day-Trading P&L Calculator: One Day to One Year
With my win rate, reward-to-risk and costs, what will a day, a month or a year of trading make — on average, typically, and in a bad year?
New from the blog
Missing the 10 Best Days
Since 1990 the S&P 500 turned $1 into $44.60, or $19.80 without its 10 best days. Miss the 10 worst too and you beat staying in. Here is why.
Four Hundred Dollars or Nine Cents
TQQQ turned $1 into $408 since 2010; a 3x S&P fund turned $1 into 9 cents in 1998–2009. The Itô formula behind leveraged ETF decay and the best leverage.
Reject Three Out of Four
The best random-walk MCMC sampler accepts 23.4% of its moves: in many dimensions it becomes a Langevin diffusion. A timid one needs 23 times the steps.
All 39 papers →All 7 notebooks →All 2 tools →All 76 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.
