Modeling Market Regime Shifts with Investor Behavior and Regulation

Summary

This document describes a continuous-time model of a single asset traded by heterogeneous agents. Its second-order dynamics represent delays between investment decisions and trades. The model includes value-based mean reversion, speculative or contrarian trading, market frictions, uncertainty about fundamental value, momentum effects, and regulatory limits on mispricing. The model produces equilibrium states, persistent price conventions, and cyclical behavior. Which regime emerges depends on the balance between value and momentum strategies, uncertainty about fundamentals, and the degree of regulation. Stochastic price paths can shift spontaneously between regimes. The account presents these outcomes as properties of the proposed framework; it gives no empirical dataset, calibration details, or quantitative tests in the supplied text, so its practical forecasting or trading value cannot be assessed from this description alone.

Key ideas

• A second-order continuous-time model represents delays between trading decisions and investment.
• The framework combines value-driven mean reversion, speculative trading, momentum, frictions, uncertainty, and regulation.
• Equilibrium, persistent conventions, and business-cycle-like price behavior can coexist.
• Relative strategy strength, fundamental uncertainty, and regulation affect which market regime occurs.
• Stochastic dynamics allow spontaneous transitions between market regimes.

Tags

# Nonlinear Dynamical Model of Regime Switching Between Conventions and Business Cycles


# Nonlinear Dynamical Model of Regime Switching Between Conventions and Business Cycles









We introduce and study a non-equilibrium continuous-time dynamical model of the price of a single asset traded by a population of heterogeneous interacting agents in the presence of uncertainty and regulatory constraints. The model takes into account (i) the price formation delay between decision and investment by the second-order nature of the dynamical equations, (ii) the linear and nonlinear mean-reversal or their contrarian in the form of speculative price trading, (iii) market friction, (iv) uncertainty in the fundamental value which controls the amplitude of mispricing, (v) nonlinear speculative momentum effects and (vi) market regulations that may limit large mispricing drifts. We find markets with coexisting equilibrium, conventions and business cycles, which depend on (a) the relative strength of value-investing versus momentum-investing, (b) the level of uncertainty on the fundamental value and (c) the degree of market regulation. The stochastic dynamics is characterized by nonlinear geometric random walk-like processes with spontaneous regime shifts between different conventions or business cycles. This model provides a natural dynamical framework to model regime shifts between different market phases that may result from the interplay between the effects (i-vi).

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