Mean-Field Price Formation on Trees with Multi-Population and Non-Rational Agents

Battle Count: 84

The paper provides a theoretically rigorous framework for understanding equilibrium price formation and the excess returns required to clear markets. While primarily theoretical, it offers insights relevant to quantitative trading: understanding how heterogeneous agent populations, external order flows, and non-rational biases affect equilibrium price distributions and fat tails. The explicit formulas for transition probabilities could inform market-making strategies and risk premium estimation. However, the single-asset, binomial-tree, CARA-utility restrictions limit direct practical implementation for most trading strategies.

The core algorithm involves backward induction on a binomial tree with finite state spaces for (S, Y, Z). The explicit formulas for transition probabilities and optimal strategies are well-defined. However, implementing the full multi-population and subjective-measure extensions requires careful handling of nested expectations, population-weighted aggregations, and the coupling between transition probability updates and the recursive value functions. The computational cost scales with the tree depth N and the number of states in Y and Z. No code is provided, requiring significant implementation effort.

The paper provides explicit analytic formulas for equilibrium transition probabilities and optimal strategies, along with detailed parameter tables (Tables 1-3) for numerical examples. However, no code repository or implementation script is provided. The backward induction procedure is fully specified mathematically, making it implementable by a skilled quantitative researcher, but reproducing the exact numerical figures would require careful coding of the recursive scheme.