Diffusion processes
How does a price move between observations? We model drift, volatility and jumps as a single process and ask what the data can actually identify about each.
Itô · Fokker–Planck · Lévy
Independent quantitative research
Research at the intersection of stochastic processes, spectral analysis and the statistics of price. Rigorous where it matters, quiet everywhere else.
Dynamics
dXt = μ(Xt, t) dt + σ(Xt, t) dWt
Density
∂t p = −∂x(μp) + ½ ∂xx(σ²p)
Spectrum
ℒf = Σk λk ⟨f, φk⟩ φk
Every project starts as a probability question. The mathematics is not decoration — it is how we decide what is signal and what is noise.
How does a price move between observations? We model drift, volatility and jumps as a single process and ask what the data can actually identify about each.
Itô · Fokker–Planck · Lévy
The eigenstructure of a generator tells you which modes decay fast and which persist. We use it to separate slow, tradable structure from fast, unforecastable motion.
Eigenvalues · Koopman · Random matrices
Estimators that are honest about their own uncertainty. Heavy tails, regime shifts and small effective sample sizes are the normal case, not the exception.
Bayesian · Robust · Extreme value
Methods
The heat kernel is the simplest diffusion there is: a point of certainty at t = 0, then a Gaussian whose variance grows linearly with time. Real markets are messier — variance is stochastic, tails are fat, the clock runs at different speeds — but the picture is the right one. Every model we build is a statement about the shape and speed of that spreading.
I
A pattern has to earn its place against a random walk with the same moments. Most do not.
II
A stochastic model is a claim about the world. It should be falsifiable on data it has not seen.
III
Volatility, volume and information arrive in bursts. The right clock is rarely the wall clock.
IV
If the derivation cannot be written on two pages, we do not trust the number at the end of it.