A model of subjective supply-demand: the maximum Boltzmann/Shannon entropy solution
نویسنده
چکیده
The present authors have put forward a projective geometry model of rational trading. The expected (mean) value of the time that is necessary to strike a deal and the profit strongly depend on the adopted strategies. A frequent trader often prefers maximal profit intensity to the maximization of profit resulting from a separate transaction because the gross profit/income is the adopted/recommended benchmark. To investigate activities that have different periods of duration we define, following the queuing theory, the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed point regardless of the shape of demand curves for a wide class of probability distributions of random reverse transaction (ie closing of the position). These conclusions remain valid in an analogous model based on supply analysis. This type of market games is often considered in the research aiming at finding an algorithm that maximizes profit of a trader who negotiates prices with the Rest of the World (a collective opponent) that posses a definite and objective supply profile. Such idealization neglects the sometimes important influence of an individual trader on the demand/supply profile of the Rest of the World and in extreme cases questions the very idea of demand/supply profile. Therefore we put forward a trading model in which the demand/supply profile of the Rest of the World induces the (rational) trader to (subjectively) presume that he/she lacks (almost) all knowledge concerning the market but his/hers average frequency of trade. This point of view introduces maximum entropy principles into the model and broadens the range of economics phenomena that can be perceived as a sort of thermodynamical system. As a consequence, the profit intensity has a fixed point with a astonishing connection with Fibonacci classical works and looking for the quickest algorithm for extremum of a convex function: the profit intensity reaches its maximum when the probability of transaction is given by the Golden Ratio rule √ 5−1 2 . This condition sets a sharp criterion of validity of the model and can be tested with real markets data. PACS numbers: 89.65.Gh, 89.70.Cf Submitted to: Journal of Statistical Mechanics – Theory and Experiments A subjective supply-demand 2
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