The Expected Utility of the Doubling Strategy

Abstract

It has been noted that a certain continuous-time trading strategy, termed the “doubling strategy”, generates a positive net return on borrowed funds, with probability one and within a finite period of time. Since the doubling strategy seems to represent a “free lunch” or arbitrage opportunity, a variety of constraints to render it infeasible have been proposed. In this paper, we show that the doubling strategy generates infinite disutility for a large class of utility functions, and we can think of no utility function for a risk-averse agent which is a counterexample.