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In credit markets, screening algorithms discriminate between good-type and bad-type borrowers. This is their raison d’être. However, by doing so, they also often discriminate between individuals sharing a protected attribute (e.g. gender, age, race) and the rest of the population. In this paper, we show how to test (1) whether there exists a statistical significant difference in terms of rejection rates or interest rates, called lack of fairness, between protected and unprotected groups and (2) whether this difference is only due to credit worthiness. When condition (2) is not met, the screening algorithm does not comply with the fair-lending principle and can be qualified as illegal. Our framework provides guidance on how algorithmic fairness can be monitored by lenders, controlled by their regulators, and improved for the benefit of protected groups.

International audience; In this article, we tackle the problem of a market maker in charge of a book of options on a single liquid underlying asset. By using an approximation of the portfolio in terms of its vega, we show that the seemingly high-dimensional stochastic optimal control problem of an option market maker is in fact tractable. More precisely, when volatility is modeled using a classical stochastic volatility model—e.g. the Heston model—the problem faced by an option market maker is characterized by a low-dimensional functional equation that can be solved numerically using a Euler scheme along with interpolation techniques, even for large portfolios. In order to illustrate our findings, numerical examples are provided.

Forest management relies on the evaluation of silviculture practices. The increase in natural risk due to climate change makes it necessary to consider evaluation criteria that take natural risk into account. Risk integration in existing software requires advanced programming skills.We propose a user-friendly software to simulate even-aged and monospecific forest at the stand level, in order to evaluate and optimize forest management. The software gives the possibility to run management scenarii with or without considering the impact of natural risk. The control variables are the dates and rates of thinning and the cutting age.The risk model is based on a Poisson processus. The Faustmann approach, including tree damage risk, is used to evaluate future benefits, economic or ecosystem services. It relies on the calculation of expected values, for which a dedicated mathematical development has been done. The optimized criteria used to evaluate the various scenarii are the Faustmann value and the Averaged yield value.We illustrate the approach and the software on two case studies: economic optimization of a beech stand and carbon sequestration optimization of a pine stand.Software interface makes it easy for users to write their own (growth-tree damage-economic) models without advanced programming skills. The possibility to run management scenarii with/without considering the impact of natural risk may contribute improving silviculture guidelines and adapting them to climate change. We propose future lines of research and improvement.