# Loan Allocation Problem

I need help with the following use case:

Context :

Let's say there is a fintech "F", that helps with aggregating personal loans. Now, "F" can pool in customers who need a personal loan. But, "F" Cannot give these loans owing to regulatory reasons. So, "F" would pass on these loans (L1, L2, L3..etc) to other Banks B1, B2...at a lower interest rate (Ex: F would originate a loan at, let's say 15% and pass on this loan to a bank at 12%. so, 3% is its profit). The banks that have the tie-up with "F" would accept loans that satisfy certain conditions like credit score, age, income-to-debt ratio, etc which we would call credit filters (CF).

A bank typically has one credit filter policy (ex: I will accept loans that are between 500 to 800 score, age between 25 - 40, income between X1 to X2, ..etc) for which they have a single rate of interest (it does not change per loan basis). Now, depending on the agreement between the fintech "F" and banks, these credit filters and the rate of interest can change. These loans are allocated by the fintech to these banks as and when these loans get applied (real-time basis). Now, while allocating so, is there a way to convert this scenario into an OR problem that has static constraints like credit filters, portfolio, and AUM but with real-time decision variables - which bank to allocate these loans to?

Example :

Objective : Maximize the ROI of the fintech "F"

Constraints :

1. credit filter of banks 1,2,3
2. Daily AUM limits for banks 1,2,3 (maximum volume of loan each bank can take per day)
3. Exposure constraints (The fintech "F" has to allocate at least 20% of its loan volume to bank 1, etc. due to the agreement)
4. Portfolio mix constraints - Ex: if bank 1 takes 20% of "F"'s loan volume, then the proportion of good, moderate, and bad credit-worthy customers has to be at 20% of the overall credit-worthy customer mix

But the catch here is the decision variables. I will have to allocate these loans in real-time. so, with such allocation, the objective has to be met, and the constraints have to be satisfied on a daily basis. Which OR methodology can help in this case?

• You are dealing with a sequential decision process, so you might want to check out this Mar 27, 2023 at 9:41