Price Optimization in Actuarial Science

Price optimization has revolutionized the conventional practice of actuarial science

Closer Consulting 

Price Optimization in Actuarial Science


Price optimization has revolutionized the conventional practice of actuarial science. This methodology allows individual variables to be integrated into the pricing process. It enables companies to tailor client proposals and to stay ahead of competitive movements.

What is actuarial science?

Actuarial science is an analytical approach to assessing financial risks in companies. It is a fundamental methodology, particularly for companies dealing with future threats. Unlike classical predictors, its guidance has a rational and accurate basis. 

Actuaries combine economic, mathematical, probabilistic and data science skills to generate forecasts and identify risks and opportunities. Although actuarial science is not the same as data science, they share many similarities. Both require the knowledge of mathematics and statistics, as well as expertise in programming and software tools.

Actuarial consulting and the importance of risk measurement

Actuarial consulting allows for calculating of both the likelihood of an event occurring and the contingency cost. It is essential, for this reason, to the financial and insurance industries. In the latter case in particular, it is indispensable in ensuring a guarantee of the solvency and competitiveness of companies.

To be viable, insurance companies need to set rates that allow them to compensate for current and future claims. Moreover, like any business, they need to generate profits and be attractive to their customers.

Consequently, pricing insurance policies efficiently involves accurately measuring risk, considering multiple assumptions and probabilities. 

Digital transformation

In just a few years, the practices and tools of actuarial science have transformed radically. Digital technologies have made it possible to process and interrelate vast amounts of data at an astonishing speed. More information makes for more accurate analyses, but processes have also become more complex.

On the other hand, technology has also changed user behavior and their level of demands. Users are now informed consumers with more accessible resources for making comparisons between different products on the market.

That is why today's challenges are about overcoming greater hurdles. Actuaries have become expert risk managers and planners.

Automation of actuarial process and tools

The definition of automation refers to delegating control of a system, process or equipment to a mechanical or electronic device.

For example, risk modelling and calculations in the insurance industry can be automated activities. While they require human knowledge for the establishment of criteria and parameters, the operations can be performed automatically. The standard actuarial tools (e.g., Emblem and Radar) can be replaced by open-source programming languages (e.g., Python) that offer more flexibility, automation and efficiency.

This means that processes and tools can be optimized by making better use of resources. Specialists save time on routine work and can focus their efforts on producing value for the company.

Ratemaking and premium definition

The contribution of actuarial science is fundamental to the setting and revision of insurance rates. For example, event observation, comparison of actual vs. budgeted expenses and market conditions, among others.

Pricing/ratemaking is a complex process, often requiring the application of several methodologies. Actuaries combine different techniques to accommodate the characteristics of various types of insurance, data constraints and regulations.

Prices in general insurance/non-life insurance

Insurance premiums or prices are closely related to risk forecasts. Variables related to the policyholder and the object to be insured are generally considered when setting costs.

Insurance pricing must ensure that coverages are guaranteed. This means that the company can respond to customers in the event of a claim. Similarly, to calculate the value of the premium, the company's operating costs and profit forecast must be estimated.

There are, however, many unknowns in this equation, which must be calibrated with precision. Underpricing certainly threatens the viability of the business, but high prices can deter customers. In fact, different studies indicate that price is the main incentive when choosing a policy. 

Expected loss and risk modelling

Predictive modelling is a technique widely used by insurance companies. It is used to assess policy risk and optimal premium pricing.

Expected losses refer to both the type and the expected economic amount of losses. These may involve the total loss of the property through theft or damage, or partial damage of property.

Statistical formulations are available to calculate risk by relating the loss (L) to the damage exposure or insurance period (e):

Predicting claims frequency and severity

The usual approach when computing risk estimates is to consider the frequency of claims and the extent of the damage, given that there is a claim.

The equation is expressed as follows:

The value “N” represents the number of claims, and “S” refers to the severity or magnitude of the damage. “F” identifies the frequency of events.


Generalized linear models

Until the mid-1980s, statistical methods were used exclusively for these calculations. Actuaries, specifically, calculated risk using the simple linear regression model, which analyzes the interdependence between variables. However, prediction with the simple regression model was not very accurate.

To overcome this pitfall, actuaries can work with two models. One analyzes the severity of the damage, while the other predicts the frequency. In both models, the dependent variable has a distribution from the exponential dispersion family (which includes the Poisson, Gamma and Normal distributions). The two results are then combined, and the risk is determined.

The evolution of this technique is the generalized linear model (GLM), which allows for the analysis of non-continuous data distributions. The introduction of a link function for non-linear dependencies enables this. Most insurance companies use GLM to determine the price of premiums.

It is easy to understand why the GLM is the industry standard. The model can be applied quickly, making its results easy to interpret. It is also a flexible scheme, capable of adapting to regulatory and operational constraints. It can even be optimized to aggregate other data types, such as customer behavior. 

Data science and machine learning

However, in recent years, machine learning has begun to displace GLM as a predictive method. The change is due to technological development and the unrelenting advance of big data. The incorporation of data science has led to a considerable improvement in forecasting.

Machine learning algorithms allow patterns’ detection and contribute to more accurate retention and conversion estimation. Their main advantage is creating algorithms from real data rather than working with assumptions. This is why logistic regressions are losing popularity to non-linear classification models in actuarial practice.

Techniques such as classification and regression trees, deep learning and flexible discriminant analysis are increasingly used. Often, these methods are combined to obtain greater predictive accuracy.

Pricing optimization

The conventional pricing process results in a pure premium, i.e., a risk-based price. Acquisition and underwriting costs and other operating expenses are then added to the expected losses.

The disadvantage of this approach is that it neglects key factors such as competition and customer behavior. Price optimization allows insurance companies to generate quotes tailored to the characteristics of potential underwriters.

Optimized pricing structures allow predicting the profitability of the business by integrating it into a single model:

  • The risk premium

  • Market analysis (competition)

  • Price elasticity

The main benefits of price optimization models are:

  • Increasing the company's profit margins

  • Generating more business

  • Increased retention rates (increased customer loyalty)

  • Improved lead conversion rates

  • Maximizing customer lifetime value

Profitability and competitivity

Price optimization can impact the current profitability of the business and favor future viability. This technique makes it possible to analyze the market environment and estimate the effect of price changes on demand. Both conditions decisively influence customer behavior.

Consider the increasing use of online rate comparison platforms. It is almost certain that, before taking out insurance, underwriters will research competitors' proposals and prices. Price optimization aims to determine the balance point between profitability and competitiveness. 

Retention and conversion

Customer conversion and retention are a priority for any industry, including the insurance sector. Actuarial science uses price optimization to estimate the likelihood of subscriber conversion and retention.

Conversion probabilities are calculated by considering both the risk premium and its position relative to the competition, as well as the demographic characteristics of potential customers. In addition to these factors, the premium and claims history of the insured is also included in the retention analysis.

The application of either model will depend on the company's business objectives at a given point in time.

Dynamic pricing

Technological advances allow a large amount of data to be processed quickly. With this information, it is possible to generate dynamic prices and offer personalized rates in real-time. In other words, calculations are automatically updated to respond to market events and customer behavior.

Insurance companies can incorporate risk-related data, performance indicators or market challenges into their pricing models. In this way, they can offer immediate and accurate solutions that ensure the long-term profitability of the business.

Given a good database, AI can determine quite accurately what price customers are willing to pay. According to an IBM study, this translates into a 2-3% increase in premiums. 

Design and management of insurance products

Price optimization is not only a tool for tariff structuring. Data analysis allows companies to identify business opportunities. By better understanding their customers' needs, they can develop new products and customize their proposals.

In any case, the industry's regulations and operational constraints must be considered. In particular markets, price optimization is considered an unfair practice and is highly monitored.



Price optimization in actuarial science is a powerful technique, providing much more accurate results than GLM models. Its implementation allows the generation of customized premiums in real-time, tailored to the customers’ needs. These can then be turned into competitive advantages that will undoubtedly impact the insurance company’s profitability.


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