# Do all credit card accounts eventually die from fraud?

Studying the lifetime of a credit card account is an interesting topic for credit card issuers. What is the natural cause of death for a credit card account? It is credit card fraud, which eventually results in the account to be killed and replaced with a new number.

Source for picture: credit card fraud

Credit card accounts can die from various causes:

• Canceled by user
• Canceled by issuer
• The user died
• The credit card is lost or unused

Yet, given enough time, a credit card account will eventually meet its natural fate: being hijacked by criminals, and die - I call this dying from old age. From a business point of view, this brings an interesting question: how do you predict, based on user segment, when a credit card will die, and how to leverage your forecast to limit losses.

Here's my proposal, based on some anecdotal evidence:

• Credit card issuer earned \$30,000 in merchant fees over all transactions
• Credit card issuer lost \$2,000 when account died because of theft

It is an interesting problem from a predictive modeling viewpoint. It is sometimes referred to as time-to-crime statistical prediction, in which exponential distributions used to model lifetime of an account, are combined with censored data (censored because future is not known) for parameter fitting, to predict time-to-crime.

Here's a quick way for an issuer to further reduce losses, based on my above example:

• Determine for each user, the time-to-crime statistic
• Offer user \$1,000 to change credit card account number 6 months before death (by crime) is expected to occur (in my example, offering less than \$1,000 might not be enough to convince the user to change, but for a smaller account, a \$20 offer might be enough)
• Instead of incurring a \$2,000 loss, the issuer will incur about \$1,000 loss (in my above example - the fee paid to the user if and only if the account number is changed before being hijacked), reducing loss by 50%

You might as well automatically change the account number after x years, but unless all issuers agree on this scheme, as an issuer, you are likely to lose users if you implement this strategy.

Question: do you know any study providing details about the lifetime of credit card accounts?

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### Replies to This Discussion

Most card issuers model account attrition due to various causes. The attrition rate due to fraud is quite small compared to the other main effects: charge-off, bankrupt, deceased, closed by request. The problem with fraud is that it is primarily an exogenous effect (random point in time), rather than an age-related effect. Examples of exogenous effects that would have to be filtered out in any model are accounts involved in the Target and Home Depot breaches. Once filtered out, is there enough data left to build a plausible model?

Resources are better spent predicting major breaches. Larger issuers may be able to spot patterns of suspicious activity at their infancy and determine the set of their cards that are at risk.

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