基于排名依赖的进出机制的股票市场中的行波
Traveling Waves in Equity Markets with Rank-Based Entry and Exit
AI总结：
该研究通过带排名依赖进出机制的几何布朗运动粒子模型，结合CRSP数据校准，证明股票市场长期资本分布为行波，且换手率稳定市场，该行波可拟合经验分布并确定多元化投资组合的资本增长。
AI中文摘要：
我们采用带几何布朗运动的粒子来建模股票市场，这些粒子以依赖于排名的强度进入和退出市场。在多公司极限下，资本分布收敛到由强度构建反应项的反应-扩散方程的解。基于CRSP数据校准后，反应项是双稳态的，长期分布为行波：我们证明了其存在性、唯一性，且对于常系数情况存在指数弛豫。校准后的市场由换手率而非漂移稳定。在实测波动率下，该行波在每个十年都能拟合经验资本分布，确定多元化加权投资组合的资本增长，并将市场置于多元化阶段的边界内。换手率抵消了再平衡带来的大部分收益。
英文摘要：
We model equity markets using geometric Brownian particles entering and exiting at rank-dependent intensities. In the many-firm limit, the capital distribution converges to the solution of a reaction-diffusion equation with reaction term built from the intensities. Calibrated on CRSP data, the reaction term is bistable, and the long-run distribution is a traveling wave: we prove existence, uniqueness, and, for constant coefficients, exponential relaxation. Turnover, not drift, stabilizes the calibrated market. With measured volatility, the wave tracks the empirical capital distribution in every decade, determines the capitalization growth of diversity-weighted portfolios, and places the market just inside the boundary of the diverse phase. Turnover reclaims most of what rebalancing gains.
