Stochastic model of brokerage customer value based on investment psychology segmentation and GARCH

The value of securities brokerage customer comes from their trading commission, which depends on their investment return rate and assets turnover rate. Both of them are influenced by customer's investment psychological characteristics and stock market return rate. For stock market return rate is a random variable, commission income also has random characteristics, deterministic models based on historical commission income does not suitable to estimate the value of brokerage customers. Using K-means cluster to segment customer with deposition effect and over confidence, stock market return rate as the random variable, a customer commission value model is given, which is based on GARCH to model every group's assets turnover rate, and a linear equation to model every group's investment return rate. Because no analytical solution can be found for this model, Monte Carlo simulation is used to find the numerical solution. The empirical results show that, relative to the deterministic model, this model can give a more accurate estimation for the long-run value of brokerage customer segment with different investment psychological characteristics, and provide a reasonable basis for enterprises to optimize their marketing and service inputs.