We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we show that, under the usual no-arbitrage condition, the existence of a replicating portfolio for a derivative implies that the latter admits a unique fair price. Then, we provide a formalization of the Cox–Rubinstein model and we show that the market is complete in this model, i.e., that every derivative product admits a replicating portfolio. This entails that in this model, every derivative product admits a unique fair price. In addition, we provide Isabelle functions to compute the fair price of some derivative products.

中文翻译：

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在 Isabelle/HOL 中将欧洲衍生品的 Cox-Ross-Rubinstein 定价形式化

我们在证明助理 Isabelle 中将金融数学的基本概念和结果形式化。我们提供了市场、投资组合、衍生产品、套利或公平价格等概念的通用形式定义，并且我们表明，在通常的无套利条件下，衍生产品的复制投资组合的存在意味着后者承认一个独特的合理的价格。然后，我们提供了 Cox-Rubinstein 模型的形式化，并证明了该模型中的市场是完备的，即每个衍生产品都允许复制投资组合。这意味着在这个模型中，每个衍生产品都有一个独特的公平价格。此外，我们提供 Isabelle 函数来计算一些衍生产品的公平价格。