The Mathematics of Capital, Inventory, Financial Capital, and Utility

This research project develops a monograph on divergent stochastic time series that permits the modeling of capital, inventory, and financial capital in economies.

Neither a textbook nor a monograph exists on divergent stochastic time series. Indeed, the primary document on divergent series is the lecture notes of G. H. Hardy. This book, still in publication by the American Mathematical Society, provides the content of his 1905-1907 lectures on divergent series at Oxford University. Existing methods of stochastic calculus are built around convergent series and are invalid for use with divergent series. The rules of modeling currently in use, where capital is a choice of marginal decision makers, give rise to a mathematical contradiction. Unlike the normal distribution, whose mean and variance converge to a specific value, the sample mean of the Cauchy distribution never settles down to a specific value. The mathematical changes in this text do more than propose a change in a statistical distribution. Instead the changes propose a radically different anthropology than would be implied if the rational expectations model could hold mathematically.