Geometric Brownian motion with intermittent entries and exits

Battle Count: 69

GBM is the foundational model for asset pricing (Black-Scholes-Merton). This paper extends GBM to open systems with entry/exit mechanisms, which is relevant for understanding market microstructure (new listings, delistings), portfolio turnover, and the emergence of heavy tails in return distributions. The first-passage time analysis and optimal exit rate findings could inform stop-loss strategies and risk management. However, the paper is primarily theoretical and does not propose a direct trading strategy. The moment regime analysis (saturation vs. exponential growth) has implications for understanding when market concentration becomes unbounded.

The analytical framework requires advanced knowledge of stochastic processes, Fokker-Planck equations, Laplace-Mellin transforms, and renewal theory. Implementing the stationary distribution (Eq. 15) and moment calculations (Eq. 19) is straightforward given the closed-form expressions. The first-passage time optimization (Eq. 49) requires solving a transcendental equation numerically. Numerical simulation of the entry-exit GBM process is moderately complex but well-defined. No code is provided.

The paper provides complete analytical formulas (Eqs. 1-49), explicit parameter values for all figures, and a detailed derivation in appendices. Numerical simulation parameters are fully specified. However, no code repository is provided. The theoretical framework is self-contained and reproducible from the equations given.