Over the last 10 years or so a mathematical theory of bubbles has emerged, following a martingale theory based on an … absence of arbitrage, as opposed to an equilibrium theory. This paper attempts to explain the major developments of the theory … recent development of a theory of bubble detection. Critiques of the theory are presented, and a defense is offered …

of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz (1959) and the capital … utility. As a result, the growth optimal portfolio theory Lintner (1965) and the leverage space portfolio theory Vince (2009 …