Background The most popular statistical model used in modeling general insurance claims is the Generalized Linear Model (GLM), introduced by Nelder and Wedderburn (1972). GLMs allow actuaries to incorporate a wide range of statistical distributions that are commonly adopted in actuarial analytics, and the underlying linearity assumption provides an explainable framework for claims modeling (Wüthrich and Merz, 2023). This model has been shown to work well in practice; however, deep learning--the subset of machine learning focusing on artificial neural network models--has been gaining substantial ground in recent years. Applications of deep learning and other novel machine learning techniques in claim modeling have shown an improvement in prediction accuracy compared to classical methods such as the GLM (Noll et al., 2020; Wüthrich and Buser, 2023). Nevertheless, the integration of such advanced techniques as the primary pricing method among actuaries has been slow since they are often perceived as "black boxes", where the intricacies of the inner workings remain obscured, making it challenging to decipher the rationale behind the models' predictions (Harris et al., 2024). Corresponding author Email address: tupho289@gmail.com

Fairness has emerged as a critical consideration in the landscape of machine learning algorithms, particularly as AI continues to transform decision-making across societal domains. To ensure that these algorithms are free from bias and do not discriminate against individuals based on sensitive attributes such as gender and race, the field of algorithmic bias has introduced various fairness concepts, along with methodologies to achieve these notions in different contexts. Despite the rapid advancement, not all sectors have embraced these fairness principles to the same extent. One specific sector that merits attention in this regard is insurance. Within the realm of insurance pricing, fairness is defined through a distinct and specialized framework. Consequently, achieving fairness according to established notions does not automatically ensure fair pricing in insurance. In particular, regulators are increasingly emphasizing transparency in pricing algorithms and imposing constraints on insurance companies on the collection and utilization of sensitive consumer attributes. These factors present additional challenges in the implementation of fairness in pricing algorithms. To address these complexities and comply with regulatory demands, we propose an efficient method for constructing fair models that are tailored to the insurance domain, using only privatized sensitive attributes. Notably, our approach ensures statistical guarantees, does not require direct access to sensitive attributes, and adapts to varying transparency requirements, addressing regulatory demands while ensuring fairness in insurance pricing.

This paper presents a novel approach to optimizing profit margins in non-life insurance markets through a gradient descent-based method, targeting three key objectives: 1) maximizing profit margins, 2) ensuring conversion rates, and 3) enforcing fairness criteria such as demographic parity (DP). Traditional pricing optimization, which heavily lean on linear and semi definite programming, encounter challenges in balancing profitability and fairness. These challenges become especially pronounced in situations that necessitate continuous rate adjustments and the incorporation of fairness criteria. Specifically, indirect Ratebook optimization, a widely-used method for new business price setting, relies on predictor models such as XGBoost or GLMs/GAMs to estimate on downstream individually optimized prices. However, this strategy is prone to sequential errors and struggles to effectively manage optimizations for continuous rate scenarios. In practice, to save time actuaries frequently opt for optimization within discrete intervals (e.g., range of [-20\%, +20\%] with fix increments) leading to approximate estimations. Moreover, to circumvent infeasible solutions they often use relaxed constraints leading to suboptimal pricing strategies. The reverse-engineered nature of traditional models complicates the enforcement of fairness and can lead to biased outcomes. Our method addresses these challenges by employing a direct optimization strategy in the continuous space of rates and by embedding fairness through an adversarial predictor model. This innovation not only reduces sequential errors and simplifies the complexities found in traditional models but also directly integrates fairness measures into the commercial premium calculation. We demonstrate improved margin performance and stronger enforcement of fairness highlighting the critical need to evolve existing pricing strategies.

Insurers usually turn to generalized linear models for modelling claim frequency and severity data. Due to their success in other fields, machine learning techniques are gaining popularity within the actuarial toolbox. Our paper contributes to the literature on frequency-severity insurance pricing with machine learning via deep learning structures. We present a benchmark study on four insurance data sets with frequency and severity targets in the presence of multiple types of input features. We compare in detail the performance of: a generalized linear model on binned input data, a gradient-boosted tree model, a feed-forward neural network (FFNN), and the combined actuarial neural network (CANN). Our CANNs combine a baseline prediction established with a GLM and GBM, respectively, with a neural network correction. We explain the data preprocessing steps with specific focus on the multiple types of input features typically present in tabular insurance data sets, such as postal codes, numeric and categorical covariates. Autoencoders are used to embed the categorical variables into the neural network and we explore their potential advantages in a frequency-severity setting. Finally, we construct global surrogate models for the neural nets' frequency and severity models. These surrogates enable the translation of the essential insights captured by the FFNNs or CANNs to GLMs. As such, a technical tariff table results that can easily be deployed in practice.

Indirect discrimination is an issue of major concern in algorithmic models. This is particularly the case in insurance pricing where protected policyholder characteristics are not allowed to be used for insurance pricing. Simply disregarding protected policyholder information is not an appropriate solution because this still allows for the possibility of inferring the protected characteristics from the non-protected ones. This leads to so-called proxy or indirect discrimination. Though proxy discrimination is qualitatively different from the group fairness concepts in machine learning, these group fairness concepts are proposed to 'smooth out' the impact of protected characteristics in the calculation of insurance prices. The purpose of this note is to share some thoughts about group fairness concepts in the light of insurance pricing and to discuss their implications. We present a statistical model that is free of proxy discrimination, thus, unproblematic from an insurance pricing point of view. However, we find that the canonical price in this statistical model does not satisfy any of the three most popular group fairness axioms. This seems puzzling and we welcome feedback on our example and on the usefulness of these group fairness axioms for non-discriminatory insurance pricing.

Intelligent automation drives the best ROI for repetitive, standardized, and attention-demanding workflows. Claims management is a great example of such. Largely paper-based and rarely end-to-end digitized, the claims management process can eat up to 50%-80% of premiums' revenues. Being primarily manual, claims processing is also prone to errors and inefficiencies, which further drive up the insurers' operating costs. As McKinsey stated at the beginning of 2019, larger insurance carriers haven't quite addressed the costs of services delivery: In particular, the increase in connectivity--telematics and onboard computers in cars, smart home assistants, fitness trackers, healthcare wearables, and other types of IoT devices--now allows insurers to automatically collect more comprehensive data from customers.

In applications of predictive modeling, such as insurance pricing, indirect or proxy discrimination is an issue of major concern. Namely, there exists the possibility that protected policyholder characteristics are implicitly inferred from non-protected ones by predictive models, and are thus having an undesirable (or illegal) impact on prices. A technical solution to this problem relies on building a best-estimate model using all policyholder characteristics (including protected ones) and then averaging out the protected characteristics for calculating individual prices. However, such approaches require full knowledge of policyholders' protected characteristics, which may in itself be problematic. Here, we address this issue by using a multi-task neural network architecture for claim predictions, which can be trained using only partial information on protected characteristics, and it produces prices that are free from proxy discrimination. We demonstrate the use of the proposed model and we find that its predictive accuracy is comparable to a conventional feedforward neural network (on full information). However, this multi-task network has clearly superior performance in the case of partially missing policyholder information. Keywords: Indirect discrimination, proxy discrimination, discrimination-free insurance pricing, unawareness price, best-estimate price, protected information, discriminatory covariates, fairness, incomplete information, multi-task learning, multioutput network.

Insurance pricing is a never-ending battle. With the advent of comparative raters in the P&C insurance market, prospects can compare prices on many companies instantly, and, not surprisingly, they usually choose the lowest offer. Inaccurate pricing is costly for insurance companies: it improves competitors' customer base, reduces customer retention, and attracts risky customers. This is why actuaries spend hours on fine-tuning pricing models. But how do actuaries actually create an insurance premium?

It is difficult to open an insurance industry newsletter these days without seeing some reference to machine learning or its cousin artificial intelligence and how they will revolutionize the industry. Yet according to Willis Towers Watson's recently released 2019/2020 P&C Insurance Advanced Analytics Survey results, fewer companies have adopted machine learning and artificial intelligence than had planned to do so just two years ago (see the graphic below). In the context of insurance, we're not talking about self-driving cars (though these may have important implications for insurance) or chess-playing computers. We're talking about predicting the outcome of comparatively simple future events: Who will buy what product, which clients are more likely to have what kind of claim, which claim will become complex according to some definition. Analytics have applications across the insurance value chain, from marketing, client acquisition and retention to underwriting, pricing and claims management, as insurers look to squeeze more signal out of their data.

Have you ever wondered whether you should be applying Machine Learning in Insurance Pricing? According to Gartner, Machine Learning is one of the hottest technology trends of 2016 and is revolutionising the way many companies do business. In this blog post I take a look at machine learning from an insurance pricing stand point, highlighting the advantages and challenges of applying machine learning in insurance pricing. In order to help you get started I also provide free R code, so you can try these exciting algorithms on your own insurance data. Machine Learning has gained in popularity in recent years - but wait... isn't Machine Learning just Statistical Modelling!? Lets start with some definitions: Clearly then there are similarities between supervised learning and statistical modelling.