Abstracts

In our previous paper ``A pricing theory on finite number of issued securities'', we capture the effect of constraint of finite number of issued securities. However, we postulated very simple model on stochastic process; one period binomial model. Binomial model is strongly related to the normal distribution. However, the normality is often denied empirically. We can observe non-normality on many kinds of assets. `Fat-tail' is the typical example. Statistics and/or mathematical finance shows several methods to describe non-normality. The simplest method for embedding non-normality is to extend binomial model to trinomial, quadinomial or higher dimensional model with the extreme lower values. However, these extreme lower values are often very difficult to capture, because this is often happened with unobservable lower probability.
Furthermore, information on such a rare event is restricted. A market participant might have sufficient information on it, while the other market participant might not. In such a circumstance, the former market participant can exactly specify the probability space by his information, while the latter market participant may construct the probability different from the probability with the sufficiently informed market participant. In this sense, asymmetry of cognition of market participants will be included in the model. In the previous paper, the difference of risk-aversions expresses the heterogeneity of market participants. In addition to this heterogeneity, we consider the heterogeneity on cognition of market participants and analyze the effect of this additional heterogeneity on security price, under the condition that there is the finite number of issued securities.
It is clear that this new heterogeneity is deduced to the problem on model risk, because model risk appears, if market participants are not necessarily to be able to exactly specify model parameters and/or structure of probability space.
Our goal is to describe the security price with the finite number of issued securities under this additional heterogeneity related to the model risk. In this paper, we formulate to control this heterogeneity utilizing the method of maxmin expected utility and derive the security price formula consistent with our previous paper.