Unstructured data are a promising new source of information that insurance companies may use to understand their risk portfolio better and improve the customer experience. However, these novel data sources are difficult to incorporate into existing ratemaking frameworks due to the size and format of the unstructured data. This paper proposes a framework to use street view imagery within a generalized linear model. To do so, we use representation learning to extract an embedding vector containing useful information from the image. This embedding is dense and low dimensional, making it appropriate to use within existing ratemaking models. We find that there is useful information included in street view imagery to predict the frequency of claims for certain types of perils. This model can be used as in a ratemaking framework but also opens the door to future empirical research on attempting to extract which characteristics within the image leads to increased or decreased predicted claim frequencies. Throughout, we discuss the practical difficulties (technical and social) of using this type of data for insurance pricing.

In pricing insurance contracts based on the individual policyholder’s aggregate losses for non-life insurers, the literature has mainly focused on using detailed information from policies and closed claims. However, the information on open claims can reflect shifts in the distribution of the expected claim payments better than closed claims. Such shifts may be needed to be reflected in the ratemaking process earlier rather than later, especially when insurers are experiencing environmental changes. In practice, actuaries use ad hoc techniques to adjust data to current levels to determine premiums. This paper presents an intuitive ratemaking model, employing a marked Poisson process framework, which ensures that the multivariate risk analysis is done more routinely using all reported claims and makes an adjustment for Incurred But Not Reported claims. Utilizing data from the Wisconsin Local Government Property Insurance Fund, we find that by determining rates based on current data, the proposed ratemaking model leads to better alignment of premiums and provides insurers with a more financially sound portfolio.

In this paper, we discuss the estimation of conditional quantiles of aggregate claim amounts for non-life insurance embedding the problem in a quantile regression framework using the neural network approach. As the first step, we consider the quantile regression neural networks (QRNN) procedure to compute quantiles for the insurance ratemaking framework. As the second step, we propose a new quantile regression combined actuarial neural network (Quantile-CANN) combining the traditional quantile regression approach with a QRNN. In both cases, we adopt a two-part model scheme where we fit a logistic regression to estimate the probability of positive claims and the QRNN model or the Quantile-CANN for the positive outcomes. Through a case study based on a health insurance dataset, we highlight the overall better performances of the proposed models with respect to the classical quantile regression one. We then use the estimated quantiles to calculate a loaded premium following the quantile premium principle, showing that the proposed models provide a better risk differentiation.

We consider the following question: given information on individual policyholder characteristics, how can we ensure that insurance prices do not discriminate with respect to protected characteristics, such as gender? We address the issues of direct and indirect discrimination, the latter resulting from implicit learning of protected characteristics from nonprotected ones. We provide rigorous mathematical definitions for direct and indirect discrimination, and we introduce a simple formula for discrimination-free pricing, that avoids both direct and indirect discrimination. Our formula works in any statistical model. We demonstrate its application on a health insurance example, using a state-of-the-art generalized linear model and a neural network regression model. An important conclusion is that discrimination-free pricing in general requires collection of policyholders’ discriminatory characteristics, posing potential challenges in relation to policyholder’s privacy concerns.

It has become standard practice in the non-life insurance industry to employ generalized linear models (GLMs) for insurance pricing. However, these GLMs traditionally work only with a priori characteristics of policyholders, while nowadays we increasingly have a posteriori information of individual customers available across multiple product categories. In this paper, we therefore develop a framework to capture this a posteriori information over several product lines using a dynamic claim score. More specifically, we extend the bonus-malus-panel model of Boucher and Inoussa (2014) and Boucher and Pigeon (2018) to include claim scores from other product categories and to allow for nonlinear effects of these scores. The application of the proposed multi-product framework to a Dutch property and casualty insurance portfolio shows that customers’ individual claims experience can have a significant impact on the risk classification. Moreover, it indicates that considerably more profits can be gained by accounting for their multi-product claims experience.

We view the retail non-life insurance decision from the perspective of the insured. We formalize different consumption–insurance problems depending on the flexibility of the insurance contract. For exponential utility and power utility we find the optimal flexible insurance decision or insurance contract. For exponential utility we also find the optimal position in standard contracts that are less flexible and therefore, for certain nonlinear pricing rules, lead to a welfare loss for the individual insuree compared to the optimal flexible insurance decision. For the exponential loss distribution, we quantify a significant welfare loss. This calls for product development in the retail insurance business.

We propose a new parametric model for the modelling and estimation of event distributions for individuals in different firms. The analysis uses panel data and takes into account individual and firm effects in a non-linear model. Non-observable factors are treated as random effects. In our application, the distribution of accidents is affected by observable and non-observable factors from vehicles, drivers and fleets of vehicles. Observable and unobservable factors are significant to explain road accidents, which mean that insurance pricing should take into account all these factors. A fixed effects model is also estimated to test the consistency of the random effects model.

This paper considers insurance claims that are available by cause of loss, or peril. Using this multi-peril information, we investigate multivariate frequency and severity models, emphasizing alternative dependency structures. Although dependency models may be used for many risk management strategies, we focus on ratemaking.

Motivation for this research comes from homeowners insurance and so, for the frequency portion, we consider binary response models. Specifically, we examine several multivariate binary regression models that have appeared in the biomedical literature, focusing on a dependence ratio model. For multivariate severity, we use Gaussian copulas to represent dependencies among gamma regressions.

We calibrate competing models based on a representative sample of over 400,000 records and validate them using a held-out sample of over 350,000 records. We find that methods that allow for cross-dependencies among perils provide important economic value in pricing.

A general ‘multivariate’ decomposition of covariances is formulated and proved, and its role in the context of financial risk measurement and pricing is demonstrated.

This paper provides an introduction to asset pricing theory and its applications in non-life insurance. The first part of the paper presents a basic review of asset pricing models, including discrete and continuous time capital asset pricing models (the CAPM and ICAPM), arbitrage pricing theory (APT), and option pricing theory (OPT). The second part discusses applications in non-life insurance. Among the insurance models reviewed are the insurance CAPM, discrete time discounted cash flow models, option pricing models, and more general continuous time models. The paper concludes that the integration of actuarial and financial theory can provide major advances in insurance pricing and financial management.