A kinetic exchange model is used to investigate the evolution of wealth distribution in a financial market. Assume that the market is characterized by a risky asset (a stock) and a risk-less asset (a bond). The model captures wealth exchanges and speculative trading to affect the dynamics of wealth distribution. We embed a suitable value function into the interactions of wealth to describe that agents allocate their wealth between the risky and risk-less assets. The value function contains the predicted price and present price of the stock to depict reactions of agents toward potential risks. The price prediction and risk estimation affect investment strategies of agents through the value function. After constructing the interactions of wealth, we apply quasi-invariant wealth limits and Boltzmann-type equations to derive a Fokker-Planck equation with underlying equilibrium. When the wealth invested in the risky asset satisfies certain conditions, an explicit stationary solution of the Fokker-Planck equation is obtained to show that the wealth distribution converges exponentially to a close lognormal distribution in the long run. Numerical experiments are given to illustrate our results.

动态交换模型用于研究金融市场中财富分配的演变。假设市场以风险资产（股票）和无风险资产（债券）为特征。该模型捕获财富交换和投机性交易，以影响财富分配的动态。我们将适当的价值函数嵌入到财富的相互作用中，以描述代理商在风险资产和无风险资产之间分配其财富。价值函数包含库存的预测价格和当前价格，以描述代理商对潜在风险的反应。价格预测和风险估计通过价值函数影响代理商的投资策略。构建财富互动之后，我们应用准不变的财富极限和玻尔兹曼型方程来推导具有基本平衡的福克-普朗克方程。当投资于风险资产的财富满足特定条件时，将获得Fokker-Planck方程的显式平稳解，以证明长期而言，财富分配呈指数收敛于接近对数正态分布。数值实验说明了我们的结果。