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I have a problem similar to what is on the title but not the same, the problem on the title allows me to explain the dynamics of my need.

I have to determine how much is the optimal value for a variable called QUOTA or LIMIT for a credit card.

The goal of the model is to allow me to minimize the probability of default, given this variable and others which caracterize my costumer. Which is the best way to determine this?

I have thought two possibilities:

  • Train a model with all the exogenous and the LIMIT as variables for any classification model (with Y=Default/No Default)
  • Train a model with all the exogenous variables but not a LIMIT (with Y=Default/No Default), then train another model with the resulting probability and LIMIT as the only two variables (with Y=Default/No Default).

Any of this possibilities sound right?

With both models, the application dataset should repeat costumers with two or more possible values for the LIMIT variable and obtain the default probability of every customer repetition. Does this sound correct?

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  • $\begingroup$ it seems to me a kind of survival analysis (where limit becomes the "time") is more appropriate $\endgroup$ – Nikos M. Feb 23 at 19:47
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    $\begingroup$ If you're just trying to minimise the probability of default with respect the limit, you'd just set the limit to $0. That way you'll never lose money since you're never lending any. What you should be trying to do is maximising profit while minimising the probability of default. $\endgroup$ – ralph Mar 2 at 14:06
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You can model it as a binary logistic regression. The target is the probability of default. One of the features is credit card limit.

Logistic regression allows an odds ratio to be calculated. The odd ratio will give the effect of increasing credit card limit on wether a default is predicted to happen.

Logistic regression allows a threshold to be set to "minimize the probability of default".

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