Financial Bubbles Existence in the Cantor–Lippman Model for Continuous Time

Abstract

This article considers the problem of bubbles existence while using the pool of renewable investment projects. The formulation of the Cantor–Lippman model for continuous time is described in this paper. The result allows to classify pools of investment projects into the arbitration, and the ineffective and the standard is proved. The estimation of the yield is found for each of the classes. The classification of pools and their yield calculation are based on the functions of the upper envelope of the Laplace transform of the investment projects cash flow functions. It is shown that for the case of a standard pool the yield can be obtained by computing the minimal positive root of the upper envelope. Also, it is shown that for the case of a standard pool the roots different from the minimum one refer to bubble strategies requiring permanent reinvesting to support growth and are not able to result in liquid final state for investors.