We explore the abilities of two machine learning approaches for no-arbitrage interpolation of European vanilla option prices, which jointly yield the corresponding local volatility surface: a finite dimensional Gaussian process (GP) regression approach under no-arbitrage constraints based on prices, and a neural net (NN) approach with penalization of arbitrages based on implied volatilities. We demonstrate the performance of these approaches relative to the SSVI industry standard. The GP approach is proven arbitrage-free, whereas arbitrages are only penalized under the SSVI and NN approaches. The GP approach obtains the best out-of-sample calibration error and provides uncertainty quantification.The NN approach yields a smoother local volatility and a better backtesting performance, as its training criterion incorporates a local volatility regularization term.

事实证明，在非洲等发展中的小额信贷可以显着改善当地经济。但是，发展领域的许多申请人无法提供金融机构要求做出贷款决定所需的足够信息。结果，小额信贷机构要根据常规政策正确分配信贷是一个挑战。在本文中，我们将小额信贷的决策制定为涉及学习和控制的严格优化框架。我们提出了一种算法来探索和学习批准或拒绝申请人的最佳政策。我们提供了保证算法融合到最佳算法的条件。拟议的算法自然可以处理丢失的信息和系统折衷的多个目标，例如利润最大化，金融包容性，社会利益和经济发展。通过对真实和合成小额信贷数据集进行广泛的模拟，我们表明我们提出的算法优于现有基准。据我们所知，本文是第一个在小额信贷和控制和使用控制理论工具之间建立连接的文章，以通过可证明的保证优化策略。