Mathematical Finance Modeling generally uses complex mathematical tools from Stochastic Processes, Partial Differential Equations, and Numerical Analysis. The COVID-19 pandemic drove the scientific community’s attention to the problem of providing realistic epidemiological scenarios, as they are crucial for decision-making and public resource allocation.  This led to the design of epidemiological models also relying on sophisticated mathematical and computational tools. In both cases, calibrating such models can be challenging due to several reasons, such as the number of unknowns, the presence of noise in the data, and the model accuracy. We shall present some techniques to address these issues and their potential connection with Bayesian Inference, Neural Networks, and Model Selection.