Mathematical Model of Stock Market Crash Based onAbductive Reasoning and Development of Cognitive Experiment on Virtual Market

C. S.皮尔士是逻辑不确定性推理的一种形式。本文将溯因推理作为人类认知偏差的一种，对股票市场的统计特征进行了研究，得出了以下结论。(1)演绎推理、归纳推理和溯因推理的三种形式与基于线性系统和广义参数估计的伴随结构之间存在着对应关系。(2)提出了溯因参数估计（APE）概念，并研究了基于APE概念的伪股市预测认知实验。APE应用于自回归过程，导出了高斯分布、柯西分布和它们的中间分布.这些结果是支持分析。我提出了一个假设，连接股票市场收益率的分布，从溯因作为人类的认知偏见的中间分布。我们安排了一个认知实验，其中142名受试者试图预测时间序列作为伪股票市场动态，Pawelzik的实验的动机。结果得到了一个符合股票市场收益率分布的实验分布。这些成果以3篇论文（包括1篇国际会议论文集）和12次学术会议口头报告的形式发表。我在SICE-SI第12届会议上获得了优秀演讲奖。此外，我还参加了电气研究所的合作研究项目，

Abduction, which is articulated by C.S. Peirce, is one of the forms of inference with logical uncertainty. I studied statistic feature of stock market derived from abduction as human cognitive bias, and I got the following conclusions.(1) There exists correspondence relation between the three forms of reasoning (i.e. deduction, induction and abduction) and adjoint structures based on linear systems and generalized parameter estimation.(2) I proposed abductive parameter estimation (APE) andstudied a cognitive experiment of pseudo stock market prediction based on APE concept. APE applied to autoregressive process derives Gaussian, Cauchy andtheir intermediate distribution. These results are supported analytically. I proposed a hypothesis which connects distributions of stock market returns to the intermediate distribution derived from abduction as a human cognitive bias. We arranged a cognitive experiment, which 142 subjects try to predict time series as pseudo stock market dynamics, motivated by Pawelzik’s experiments. As a result, we obtained anexperimental distribution which conforms to one of stock market returns. These achievements were published by 3 articles (including 1 proceeding of international conference) and 12 verbal presentations in academicconferences. I was awarded the prize of excellence presentation in the 12th Conference of SICE-SI. Moreover, I join the Cooperative Research Project Program of the Research Institute of Electrical