Stationary Distributions of the Mode-switching Chiarella Model

Battle Count: 75

The paper provides deep theoretical understanding of when and why price mispricing distributions become bimodal (indicating regime-switching between over- and under-valuation), which is directly relevant to mean-reversion trading strategies, momentum strategies, and regime detection. The disproof of the equivalence between Hopf-bifurcation and P-bifurcation conditions has practical implications for calibrating agent-based models used in quantitative finance. However, the paper is primarily theoretical and does not propose specific trading algorithms or backtests.

The analytical framework involves advanced stochastic calculus (Itô processes, Fokker-Planck equations, Lyapunov equations, Furutsu-Novikov theorem, Maxwell-Boltzmann ansatz, Arrhenius law). Implementing the numerical verification requires careful Euler-Maruyama integration with appropriate time steps and long simulation horizons (T up to 10^9). The multiple parameter regimes and their validity conditions add complexity. However, the core model is a 3-dimensional SDE system that is straightforward to simulate.

The paper provides complete analytical derivations with explicit formulas for stationary distributions in multiple parameter regimes. All numerical simulation parameters (κ, β, α, γ, σ_N, σ_V, T, dt, g) are specified for each figure. The Euler-Maruyama scheme is stated for stochastic integration. Appendices contain full proofs. However, no code repository is provided, and the exact solution in the strong-coupling regime (Θ > Θ_c) is not available analytically.