Why simulate alternative paths?
Many analysis begins with a single realized history. Markets, experiments, and complex systems each leave behind one path through time, yet many other paths were possible.
By generating and studying plausible alternatives, we can ask different questions:
- How dependent are our conclusions on the particular sequence of events?
- Which observations are robust, and which are artifacts of a single realization?
- What changes when a time path unfolds differently?
Pathspace Lab explores these questions through simulation.
Start Here
If you’re new to Pathspace Lab, the best introduction is the essay:
Beyond the Realized Path
It tells the story that motivated this project, from building equity risk models to asking a deceptively simple question:
How much of what we believe depends on the single history we happened to observe?
Research Artifacts
Artifact 01
Is a minimum-variance portfolio stable under alternative realizations of the same market history?
Risk Model Framework
Building reusable tools for factor decomposition and covariance estimation.
Alternative Path Generator
An evolving simulation engine for generating plausible market histories.
Why Pathspace?
The name comes from mathematics and physics, where a pathspace is the collection of all possible paths a system can take through time.
My interest in the idea predates finance. During graduate school I studied stochastic processes in biophysical systems, where individual molecules, proteins, and ion channels evolve along many possible trajectories rather than a single predetermined path.
Markets share a similar property. We observe one realized history, but countless others were possible.
Pathspace Lab grew from that simple observation.
Research in Progress
Every artifact on this site is part of a larger question:
How much of what we believe depends on the single history we happened to observe?
Pathspace Lab is an ongoing attempt to explore that question through simulation, software, and writing. The work is shared incrementally, with each project contributing another piece of the picture.
If these questions interest you, I’d welcome the opportunity to connect, collaborate, or simply exchange ideas.