Posts by Collection

A sequential calibration monitor for probabilistic forecasts.

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.

In multiplicative wealth dynamics, “equal and opposite” moves correspond to multiplying and dividing by the same factor, not adding and subtracting equal amounts. We show that if an agent is geometrically risk-neutral in the sense that at any wealth level \(w\), they are indifferent between keeping \(w\) and taking a zero time-average growth bet, then their utility must be affine in \(\ln (w)\), hence \(u(w) = \alpha \ln (w) + \beta\).