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不对称信息随机微分博弈的充要最大值原理及其在高频金融市场中的应用
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Abstract:
本文研究了一类多人不对称信息下的非零和随机博弈问题，其中系统方程是由布朗运动驱动的随机微分方程来描述，博弈者获取信息存在延迟且不对称。利用凸变分推导了充分和必要最大值原理，给出了纳什均衡点的充要条件。进一步将理论结果应用于高频金融市场中算法交易商、一般交易商和做市商的不对称随机微分博弈。
In this paper, we investigate a class of non-zero-sum stochastic differential games with asymmetric information for multiple players, where the system equations are described by stochastic differential equations driven by Brownian motion. The players experience delayed and asymmetric information acquisition. By employing convex variation, we derive sufficient and necessary maximum principles to provide optimal conditions for the Nash equilibrium. The theoretical results are further applied to asymmetric stochastic differential games for algorithm traders, general traders, and market traders in high-frequency financial markets.
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