The paper addresses the problem of providing a framework and an algorithm to evaluate super and sub replicating prices, for European options, having interesting risk-reward characteristics. A general operational framework is put forward and illustrated by an algorithmic construction of one-dimensional models for option pricing. Asset models are defined based on a class of investors characterized by how they operate on financial data leading to potential portfolio rebalances. Once observable variables are selected for modeling, necessary conditions constraining these variables and resulting from the operational setup are derived. Future uncertainty is then reflected in the construction of combinatorial trajectory spaces satisfying such constraints. As the risky asset unfolds, it can be tested dynamically for the validity of observable sufficient conditions that rigorously imply the validity of the models. The paper describes the resulting algorithmic construction of such trajectory spaces and, in the absence of probability assumptions, a minmax algorithm that is available to evaluate the super and sub replicating prices.

中文翻译：

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带有运营假设的弹道资产模型

本文探讨了提供具有有趣的风险收益特征的欧式期权的框架和算法来评估超级和次级复制价格的问题。提出了一个通用的操作框架，并通过一维期权定价算法的算法构造进行了说明。资产模型是根据一类投资者定义的，该类投资者的特征在于他们如何处理导致潜在的投资组合再平衡的财务数据。一旦选择了可观察变量进行建模，就可以得出约束这些变量并从操作设置中得出结果的必要条件。然后，在满足这种约束的组合轨迹空间的构造中反映了未来的不确定性。随着风险资产的发展，可以动态测试可观察到的充分条件的有效性，这些条件严格暗示了模型的有效性。本文描述了这种轨迹空间的最终算法构造，并且在没有概率假设的情况下，描述了可用于评估超级和次复制价格的minmax算法。