Value versus price of an asset: is an expected utility representation possible?

We modelize the value of a financial asset as a superposition of n possible prices the asset may have. The superposition depends on weights each decision maker allots to each of the n prices influencing the value. Those n weights are complex numbers and the summation (over n weights) of the squared absolute value of the weights must be unity. Furthermore, we also show that the uncertainty on a value measurement must have a lower bound. Now to connect our proposal to basic economic theory we first consider the classical demand function of individual i which is a function of price, endowments, and preferences. In our proposed framework where we consider the value of an asset, the demand function of individual i is now still a function of price and endowments but this time the preferences are replaced by the weights making up the value of the asset. As is well established in economics, an expected utility representation capturing preferences exists whether we work in a von-Neumann Morgenstern, Anscombe-Aumann or Savage preference framework. The type of probability used in the three above frameworks varies however. A first challenge consists in answering what type of probability our framework implies. For instance, probability is a function of the lower bound to which the uncertainty on the value measurement must conform to. A second challenge is to answer the difficult question whether an expected utility representation exists when we consider the weights making up the value of the asset. We begin also to address this issue in this paper