Arash Fahim
SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Arash Fahim Abstract. "All models are wrong but some are useful", George Box 1978. Choosing a model is usually a tradeoff between tractability and capturing the reality of data. Although there is a constant tendency toward improvement of the models, the tractability imposes a firm obstacle. Therefore in many practices, there is a demand to quantify the amount of risk that we take by choosing a specific model. In finance, where the probabilistic models are very popular, choice of a model is equivalent of choosing a certain probability distribution, which is (to some extent) consistent with the data. The ones that we choose are tractable. However, there are other probability measures which are also consistent with the data, but are not tractable. In measuring the model risk, we at least try to find the extreme cases so that we can measure model risk. In finance, the problem of quantifying model risk is related to the optimal transportation theory through the Fenchel-Moreau duality; the dual problem is the problem of hedging a specified market risk using the available securities, while the primal problem is the optimal transportation problem under data/theory driven constraints. |