保证金约束下资产定价模型的广播式异步算法研究

Asynchronous Broadcast-Based Algorithm for Capital Asset Pricing Model with Margin Requirements

有保证金约束的资本资产定价模型在实际应用中面临着两个挑战,一是模型引入了非线性的约束条件,导致没有解析的均衡价格,二是市场中投资者和资产的数量都很庞大,如何高效地找到近似解。针对有保证金约束的资本资产定价模型,提出适用于多服务器协同运算的广播式异步算法。该算法把投资者分成若干个不同的组,各组在不同的服务器上独立运行,组与组之间通过网络相互传递外部价格信息,各组内部根据现有的价格和接收到的外部价格信息重新更新组内价格,并广播给相邻的组,减少了单台服务器的计算负担。该算法可看成一个非做市商的价格形成过程。研究证明,在满足一定的条件下,各组价格均以概率1收敛到相同的均衡价格。数值实验验证了所提算法的效果。

The application of the capital asset pricing model with margin-requirement constraints in practice faces two challenges.One is that the model introduces non-linear constraints,leading analytic equilibrium prices unable to be derived.The other one is that the number of investors and available assets in the market is generally very large,raising the question of how to find an approximate solution efficiently in a promising time.In this paper,we propose an asynchronous broadcast-based algorithm for the capital asset pricing model with margin-requirement constraints,which is suitable for implementing on multi servers who can work collaboratively.The algorithm divides investors into several different groups,each of which runs on an independent server to reduce the computational burden of a single server.The groups transmit prices information to each other through the network.Each group updates prices by combing their current prices with the received neighbors′prices,and broadcasts them to its neighbors.We prove that under certain conditions,each group′s prices will converge to the same equilibrium prices with probability 1.The numerical experiments verify the effectiveness of our proposed algorithm.