From Predictive to Prescriptive Through Mathematical Optimization

Imagine you have a magical tool that allows you to build a perfect model of the world – as precise as you wish. A model that can give you all the answers about the future. It can tell you anything! Just ask, “Is it going to rain tonight?” Or even better, “What will the price for oil be tomorrow?” And now, with the answers in hand, you can decide what to do next. Of course, your decision would depend on your personal targets and preferences. For example, if you want soaked clothes, the action is going to be different from that if you want to stay dry.

This shows that it is just not enough to have a perfect predictive model, no matter how precise it is. You should also know what you want to achieve and what actions you want to take based on these predictions. In practice, an analyst should make an important step – to move from predictive to prescriptive analytics. For example, think of a bank that tries to increase its volume of booked loans. After some thorough work, the bank developed models that can score and predict risk of any customer. Now using these models, they want to know what maximal volume they can reach if they want to keep risk at a certain level. There are different ways to influence overall volume of booked loans but specifically here, the bank needs to set its credit limit strategy knowing that offering higher credit limits would generally lead to higher volume of booked loans – but at the same time would also lead to an increase in overall level of risk. In general, their question is: “What are the individual credit limit terms that should be set for a customer so that the total volume is maximized without increasing the overall risk level?” To answer this type of question, we need to use math. Specifically, mathematical optimization.

The models and the assumptions can be very different. In some cases, the analyst is free to suggest different individual credit limits to customers. In others, the credit limits are defined according to customer segments or are required to follow a certain structure; for example, be monotonic – increasing or decreasing – with risk levels. Sometimes the optimized function has “nice” mathematical properties and is continuous and twice differentiable – smooth – like the simple parabola we studied in high school. And in other cases, it is not even continuous, which gives mathematicians a headache. Some analysts need to develop a holistic strategy covering new and existing customers, while others need to take care of only one of these groups. Often there are additional restrictions, as the analyst might be interested in keeping the average conversion or risk on a certain level. In addition, there could be specific ranges for credit limits for different segments. Of course, there might be other combinations and variations of constraints that we need to account for, and we still have said nothing about regulation that differs from market to market and can require that the credit limit strategy follows a certain transparent structure.

Although the objective for these types of problems is typically the same, that is, a healthier book of business balancing various KPIs such as revenues, volumes and risk levels, the methods can differ dramatically. If all the models are mathematically “nice” – such that we have the luxury of a convex differentiable function (remember the parabola?) – the tool exploits gradient-based methods to find optimal prices. If the resulting function is more challenging, e.g., lacking continuity, the analyst can define a level of precision, and the algorithm will look for the best solution on the pre-defined grid. In this case, the problem is solved using Integer Programming techniques, i.e., when the decision variable is discrete and not continuous. Alternatively, such problems can be solved using a simulation-based approach, such as Genetic or Evolutionary algorithms. Usually these are difficult problems to solve and require special tools capable of tailoring the right optimization approach for each problem.

Earnix offers solutions tailored specifically to address a wide array of mathematical optimization problems in the banking and insurance industries while considering different use cases and scenarios. It allows analysts to model the business environment using a wide range of available modeling solutions and to then find the best possible course of action or strategy using different optimization algorithms. Users can apply various algorithms to solve their business problems, but it is important to understand the structure and context of the models to select the most appropriate algorithm.

Looking at our customers, we are convinced that such an approach that combines a holistic view on modeling and mathematical optimization has great advantages. Mathematical optimization is a very powerful analytical technology that, together with machine learning and advanced statistical models, brings great results by allowing analysts and managers to run and simulate different scenarios, see how their KPIs are affected and ultimately select the best course of action.

Almost as if they were looking into a crystal ball.

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