The Expected Utility of the Doubling Strategy
证明，在连续时间交易中，加倍策略虽然能以概率1在有限时间内产生正收益，但对一大类效用函数会产生无限负效用，且不存在风险厌恶者的效用函数能作为反例。
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.