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A Cowboy’s Charm

Under multiplicative wealth dynamics, “equal and opposite” moves are multiplying and dividing, not adding and subtracting. Let’s show that any utility function that respects this fact must be affine in \(\ln w\).

“I don’t remember ever having seen a bird asking an ornithologist how to fly.”

A small tensor autograd engine and neural network library.

This thesis develops a proof of concept for a non-parametric Bayesian trade structuring system that translates an investor’s distributional views about an underlying asset into an implementable position using listed options. Starting from a market-implied prior recovered from listed option prices, the framework incorporates subjective views as constraints to construct a posterior distribution that deviates minimally from the prior while enforcing the view set. The resulting posterior is then used to derive an optimal target payoff profile under objectives such as expected log growth, and to approximate that payoff using practical option structures under real-world constraints like transaction costs and existing portfolio exposures.

Practitioners monitoring deployed probabilistic models face a fundamental trap: any fixed-sample test applied repeatedly over an unbounded stream will eventually raise a false alarm, even when the model remains perfectly stable. Existing methods typically lack formal error guarantees, conflate alarm time with changepoint location, and monitor indirect signals that do not fully characterize calibration. We present PITMonitor, an anytime-valid calibration-specific monitor that detects distributional shifts in probability integral transforms via a mixture e-process, providing Type I error control over an unbounded monitoring horizon as well as Bayesian changepoint estimation. On river’s FriedmanDrift benchmark, PITMonitor achieves detection rates competitive with the strongest baselines across all three scenarios, although detection delay is substantially longer under local drift. Code is available at https://github.com/tristan-farran/pitmon.