Bubbles in discrete-time models
提出离散时间模型中泡沫的新定义，基于折现股价在等价鞅测度下有限回撤时失去质量，并给出等价概率刻画、马尔可夫情形下的解析条件，以及该定义与连续时间严格局部鞅泡沫定义的一致性。
Abstract We introduce a new definition of bubbles in discrete-time models based on the discounted stock price losing mass under an equivalent martingale measure at some finite drawdown. We provide equivalent probabilistic characterisations of this definition and give examples of discrete-time martingales that are bubbles and others that are not. In the Markovian case, we provide sufficient analytic conditions for the presence of bubbles. We also show that the existence of bubbles is directly linked to the existence of a non-trivial solution to a linear Volterra integral equation of the second kind involving the Markov kernel. Finally, we show that our definition of bubbles in discrete time is consistent with the strict local martingale definition of bubbles in continuous time in the sense that a properly discretised strict local martingale in continuous time is a bubble in discrete time.