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Things you always wanted to know about Mathematical Optimisation for credit, but were too afraid to ask…

In this blog, we explore and address frequently asked questions about Mathematical Optimisation as it pertains to lending and collecting.

  1. What exactly is “Optimisation”?

“Optimisation” is an advanced mathematical technique used to find certain best values to improve a business problem.  It is used in a variety of industries to solve a variety of business challenges.

In the credit space it has been used for (amongst other things):

  • setting optimal loan amounts to offer (term credit products),
  • deposit amounts to request (secured lending),
  • credit limits and overdrafts to set (revolving),
  • credit limit decreases and limit increase offers (revolving),
  • authorisation strategies (revolving),
  • pricing of loans,
  • customised discounts to offer (cards and retail),
  • vouchers to offer (retail marketing),
  • calculating collection settlement amounts, and
  • calculating minimum instalment amounts in collections.

For example, we may need to find the best individual credit limits to offer each of our customers. The goal will be to boost the profitability of the business while reducing bad debt, adhering to lending legislation, reducing attrition, increasing spend and not over-indebting customers to the point where they can’t pay.

Essentially, Optimisation is a big mathematics’ problem.

  1. How is this different to using a scorecard?

Scorecard strategies tend to be a lot less complex than Optimisation.

Optimisation typically uses a variety of models with the strategy design – this may include multiple scorecards, affordability models, action-effect models, local constraints (e.g. credit limits cannot exceed $25,000) and global constraint conditions (e.g. the sum of all limit increases must be less than $100,000,000).

Traditionally, scorecards and analytical strategy design tools use historic data to predict likely behaviour, but inherently assume the observations will be treated as they were in the past. Optimisation analyses all the potential relationships that exist between the profile characteristics and the potential terms of business (strategy treatments) in order to build an optimised strategy that maximises the business objective (e.g. profit) within the client’s portfolio constraints. Action effect modelling is used to determine the impact of decisions at an account level.

  1. What type of business problems can Optimisation solve?

Optimisation has some truly remarkable applications in industry and beyond. Within credit, Optimisation has been proven to provide significant lift when applied throughout the credit lifecycle. At any point where a decision is taken, Optimisation can assist in making the best decision:

  • Which customers to target / how to target them
  • How much to offer the customer at what price
  • When and by how much to increase/decrease a customer’s limit
  • Through all of the decision points within the collections flow (When to contact/How to contact/what to offer/dialler optimisation)

The scope for Optimisation within non-traditional “non-credit” areas is very wide. Optimisation can also contribute significantly to making operational processes more efficient.  Some industries and applications are noted below:

  • Logistics – finding the optimal flying/shipping routes for passengers, freight
  • Machine processing – e.g. optimise the use of machines (e.g. printers, generators), to schedule maintenance and to improve output
  • Working schedules – used in hospitals and factories
  • Viability models – determining viability models of mines, machines
  • Pricing models – used in the airline industry to price tickets
  1. How do I know if my business is ready for Optimisation?

The following is a check-list of requirements to ensure that a lending business is Optimisation-ready.

  • Organisation has a business strategy in the area (e.g. collections), already utilising scores.
  • The Credit team is in agreement on what the constraints are (for example what is the maximum bad-debt acceptable to the company, what is the maximum limit amount allowed, what is the total capital available for lending over the next year).
  • Requires the Credit/Finance team to define the drivers of the objective (usually profit).
  • A minimum of one years’ account level data (although 2-3 years’ is preferred).
  • The ability to implement an automated decision strategy (ideally deployed through an enabling technology such as DecisionSmart)
  • Requires an organisational commitment to implement a test, if successful.
  • Another key requirement is that the organisation should ideally have run some tests. For example, if you wanted to optimise settlement amounts in collections, you will need to run some tests where you offer different settlement options to clients (e.g. 60%, 80%, 100% of balance) instead of a single strategy (for example 100% of balance). If you do not have this in place it is worth running a randomised allocation.
  1. What kind of results has Principa witnessed after the implementation of an Optimisation  strategy?

 A recent Principa Optimisation challenger strategy increased revenue by 15% and reduced delinquency by 10% (actual ROI of above 7).

  • Another Principa Optimisation challenger strategy developed in account management has increased profit per up to date account by 4% and reduced delinquency by 5% (ROI of 13.7).
  • A Principa Optimisation challenger strategy developed for new business limit setting has increased profit by 10% and reduced delinquency by 3%. 
  1. What do you need to implement an Optimisation strategy?

 Specifically (data, analytics, reporting, system(s), size of book, other considerations)

A few things need to be in place in order for an Optimisation strategy to be feasible.  If not possible then “principles of optimisation” could also be adopted.

  1. Sufficient data– the organisation will need rich data and a sufficient number of accounts on which to model.
  2. A clear objective– what are you looking to achieve? Maximise profit, minimise risk, minimise the number of staff are all examples of popular Optimisation problems in this space. Furthermore, the limitations and constraints of the business should be understood (e.g. it is bank policy not to breach a bad rate of 15%, there is only a maximum of $10,000,000 allocated for credit limit allocations, each account may have a maximum credit limit of $10,000, customer cannot breach government prescribed affordability/debt-burden-ratio thresholds).
  3. Analytics – the organisation/vendor will need to be able to build a variety of data driven models. The organisation will also need to be able to model the optimisation problem utilising suitable software.  Examples of this software include FICO’s Model Builder and Decision Optimizer, SAS and R.
  4. Deployment– the organisation will need to be able to deploy a strategy in their environment using their own (or a vendor’s) business rules management system. The system should be able to deploy complex strategies utilising decision trees, scorecards and calculations.  It should also be able to run a randomised champion/challenger testing within the environment.  If a complex decisioning environment already exists (e.g. with multiple tests running for other purposes) it should be assessed whether an Optimisation strategy can be deployed without upsetting the other tests.
  5. Monitoring – the organisation will need to be able to monitor the Optimisation strategy to determine how well it is doing when compared to the hold-out-sample. Optimisation is a cycle – each generation of models takes you to a more optimal strategy. Monitoring is key to determine which model is working best.


With a little foresight and preparation, mathematical Optimisation is within the reach of many lenders and collectors. If you are not ready now, then steps can be introduced and followed to ensure your readiness within a year or two.

To find out more about Principa’s Mathematical Optimisation offering, get in touch with us.


Thomas has 18 years’ experience in data science focusing in the EMEA region. His experience traverses multiple industries and disciplines covering analytics, consulting and software solutions for companies ranging from large banks and retailers to telcos and manufacturing operations. A large part of his experience comes from working with credit providers helping them harness the predictive power of data through the use of machine learning and decision tech. Thomas holds an MA Mathematics from Edinburgh University.