Before revision:  We modify this model using Capital Asset Pricing Model : The market exposure depends on the rank, and the benchmark moves as a general L\'evy process. We show that this model fits real market data. We discuss stability and long-term convergence .
After revision:  We modify this model using Capital Asset Pricing Model for size deciles from Center for Research in Securities Prices database, and construct a related continuous-time model for Stochastic Portfolio Theory with rank-based Levy particles. We regress equity premia for size deciles over the equity premium for the top decile, and modify the model for continuous time. We simulate the resulting capital distribution curve .