We present a number of examples and counterexamples to illustrate the results on cost-efficiency in an incomplete market obtained in [BS24]. These examples and counterexamples do not only illustrate the results obtained in [BS24], but show the limitations of the results and the sharpness of the key assumptions. In particular, we make use of a simple 3-state model in which we are able to recover and illustrate all key results of the paper. This example also shows how our characterization of perfectly cost-efficient claims allows to solve an expected utility maximization problem in a simple incomplete market (trinomial model) and recover results from [DS06, Chapter 3], there obtained using duality.

翻译：本文通过一系列示例与反例，阐释[BS24]中关于不完全市场成本效率的研究结果。这些示例与反例不仅直观展示了[BS24]的结论，同时揭示了相关结论的局限性及关键假设的严格性。特别地，我们构建了一个简单的三状态模型，该模型能够复现并阐释原文所有核心结论。此示例还表明，通过对完全成本效率权益的刻画，可以解决简单不完全市场（三项式模型）中的期望效用最大化问题，并复现[DS06, 第三章]中运用对偶方法获得的结果。