Author

Tim Gebbie

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Preprint Oct 2026

A Finite Bid--Ask Spread from Replenishment Displaced from the Quote

We give a unified analytic account of a finite bid--ask spread in a two-field reaction--diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determine...

C. Angstmann, Derick Diana, Tim Gebbie · 0 citations

Preprint Aug 2026

Reflexivity from Hierarchical Causality

Complex systems are often organised into hierarchies whose internal interactions are stronger or faster than interactions across levels. When markets are treated as genuinely multilevel systems it becomes natural to represent them as systems with hierarchical causality. Here we show that reflexivity can be formulated w...

Tim Gebbie · 0 citations