Abstract: When the stock prices or stock returns has no exact probability distribution or insufficient statistics, the online stock investment problem has obtained widespread concern. That is, investors are able to adopt online algorithm and competitive analysis to design better online investment strategies when dealing with various uncertain stock prices. This paper introduces the cognitive bias of investor's overconfidence preference into the issue of stock online investment, constructs the game models of both off-line opponents and stock online investors, and gives the optimal mixed strategies and mixed strategies Nash equilibrium under the general situation and the situation of momentum effect, respectively. The results finds that, the optimal mixed strategies under both situations not only overcome the over-dependence of traditional stock investment strategies on the assumption of stock price or probability distribution of stock returns, but also better abstract the characteristics of online investors, i.e. overconfidence and blindly gamble. This research is a useful supplement to the existing researches on behavioural finance and financial busy transactions.

Key words: online algorithm, stock investment, overconfidence, momentum effect

摘要： 当股票价格及收益的统计信息不足或无法构建精确概率分布时,股票占线投资问题获得广泛关注,即投资人能够运用在线算法和竞争分析设计出更好的占线投资策略以应对股价的不确定性。本文将投资人过度自信偏好这种认知偏差,引入到股票占线投资问题中,构建了离线对手与股票占线投资人的博弈模型,分别给出一般情形和存在动量效应情形下的最优混合策略和混合策略纳什均衡。结果发现,两种情形下的最优混合策略不仅克服了传统股票投资策略对股价或股票收益概率分布假设的过度依赖,并且更好地抽象了股票占线投资人过度自信、追涨杀跌等特征,对现有行为金融与金融占线交易问题的研究提供了有益补充。

关键词: 占线算法, 股票投资, 过度自信, 动量效应