Utility-indifference approach is a useful approach to be adopted for pricing financial derivatives in an incomplete market and is an ongoing hot research topic in quantitative finance. One interesting question associated with this approach is whether or not it renders to the same option prices, degenerately, when the market becomes infinitesimally close to a complete market. The answer for such a question has been provided for European-style options as there is a well-documented theoretical proof in Davis et al. (1993). However, a theoretical proof for the case of pricing American-style options is unavailable at this stage and the answer for this question must be at least numerically confirmed before it can be comfortably used to price American-style options in incomplete markets. The contribution of this paper is to provide such a numerical verification.

效用差异化方法是在不完全市场中对金融衍生产品定价的一种有用方法，并且是量化金融中一个持续的热门研究主题。与这种方法相关的一个有趣的问题是，当市场无限接近整个市场时，它是否会退化为相同的期权价格。戴维斯（Davis）等人提供了有据可查的理论证明，为欧式期权提供了此类问题的答案。（1993）。但是，现阶段尚无有关定价美式期权情况的理论证明，必须至少在数字上确认该问题的答案，然后才能在不完整的市场上轻松地对美式期权进行定价。