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

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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