Naoki Takata
January 13, 2026
We present a formal mathematical framework for optimal market making strategies, encompassing three interconnected models: (1) the Market Making with Alpha Signals model incorporating predictive signals, (2) the Adverse Selection with Price Reading model, and (3) the classical Avellaneda-Stoikov model. For each model, we rigorously define the parameter spaces, derive the Hamilton-Jacobi-Bellman (HJB) equations, and establish the optimal control formulations. We also present the ansatz for the value function and the optimal quote adjustment formulas.
As a proof of existence for this paper, the Keccak-256 hash of the PDF has been recorded on the Ethereum blockchain.
Timestamp: January 13, 2026 (date recorded on the blockchain)
The formal definitions and equations presented here have been verified through mechanized proof in the Lean theorem prover.
Naoki Takata
X: @naokitakata
Email: [ntakata [at] proton.me]
This is a preprint. Comments are welcome!