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Not sure if this would come under your defintion of an "open problem", but in the financial risk space there are many time consuming and costly challenges implementing economic capital models.

These models are used to determine the probability of an account/customer/contagion risk group defaulting (aka PD) and the loss incurred, given a default (LGD).

The current models require a lot of historical data to train them, and need to incorporate economic cycle factors.

There are some vendors in this space, but their products are very dated, expensive and leave a lot to be desired. Also the products really provide a platform for an actuarial team to build upon, rather than having an out of the box solution (which is probably desirable in the banking space)

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