Thanks to its outstanding performances, boosting has rapidly gained wide acceptance among actuaries. Wüthrich and Buser (Data Analytics for Non-Life Insurance Pricing. Lecture notes available at SSRN. http://dx.doi.org/10.2139/ssrn.2870308, 2019) established that boosting can be conducted directly on the response under Poisson deviance loss function and log-link, by adapting the weights at each step. This is particularly useful to analyze low counts (typically, numbers of reported claims at policy level in personal lines). Huyghe et al. (Boosting cost-complexity pruned trees on Tweedie responses: The ABT machine for insurance ratemaking. Scandinavian Actuarial Journal. https://doi.org/10.1080/03461238.2023.2258135, 2022) adopted this approach to propose a new boosting machine with cost-complexity pruned trees. In this approach, trees included in the score progressively reduce to the root-node one, in an adaptive way. This paper reviews these results and presents the new BT package in R contributed by Willame (Boosting Trees Algorithm. https://cran.r-project.org/package=BT; https://github.com/GiregWillame/BT, 2022), which is designed to implement this approach for insurance studies. A numerical illustration demonstrates the relevance of the new tool for insurance pricing.

Telematicsdevices installed in insured vehicles provide actuaries with new risk factors, such as the time of the day, average speeds, and other driving habits. This paper extends the multivariate mixed model describing the joint dynamics of telematics data and claim frequencies proposed by Denuit et al. (2019a) by allowing for signals with various formats, not necessarily integer-valued, and by replacing the estimation procedure with the Expected Conditional Maximization algorithm. A numerical study performed on a database related to Pay-How-You-Drive, or PHYD motor insurance illustrates the relevance of the proposed approach for practice.

Rough sleeping is a chronic experience faced by some of the most disadvantaged people in modern society. This paper describes work carried out in partnership with Homeless Link (HL), a UK-based charity, in developing a data-driven approach to better connect people sleeping rough on the streets with outreach service providers. HL's platform has grown exponentially in recent years, leading to thousands of alerts per day during extreme weather events; this overwhelms the volunteer-based system they currently rely upon for the processing of alerts. In order to solve this problem, we propose a human-centered machine learning system to augment the volunteers' efforts by prioritizing alerts based on the likelihood of making a successful connection with a rough sleeper. This addresses capacity and resource limitations whilst allowing HL to quickly, effectively, and equitably process all of the alerts that they receive. Initial evaluation using historical data shows that our approach increases the rate at which rough sleepers are found following a referral by at least 15% based on labeled data, implying a greater overall increase when the alerts with unknown outcomes are considered, and suggesting the benefit in a trial taking place over a longer period to assess the models in practice. The discussion and modeling process is done with careful considerations of ethics, transparency, and explainability due to the sensitive nature of the data involved and the vulnerability of the people that are affected.

Pay-how-you-drive (PHYD) or usage-based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and other driving habits. These data are collected while the contract is in force with the help of telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being incorporated in the score as ordinary a priori observable features. This paper proposes the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.

This paper investigates equilibrium in an insurance market where risk classification is restricted. Insurance demand is characterised by an iso-elastic function with a single elasticity parameter. We characterise the equilibrium by three quantities: equilibrium premium; level of adverse selection (in the economist's sense); and “loss coverage”, defined as the expected population losses compensated by insurance. We consider both equal elasticities for high and low risk-groups, and then different elasticities. In the equal elasticities case, adverse selection is always higher under pooling than under risk-differentiated premiums, while loss coverage first increases and then decreases with demand elasticity. We argue that loss coverage represents the efficacy of insurance for the whole population; and therefore that if demand elasticity is sufficiently low, adverse selection is not always a bad thing.

Risk terminology varies from organisation to organisation, and actuaries working in different organisations may use different terms to refer to the same risk, or use the same nomenclature for completely different risks. This paper sets out a classification system developed by the Risk Classification Working Party for the Profession that can be used as a common reference point for discussing risk. Actuaries will not be required to use this system, but it is hoped that common terminology will reduce the possibility of confusion in discussing risks.

This paper investigates the effects of high or low fair-premium demand elasticity in an insurance market where risk classification is restricted. The effects are represented by the equilibrium premium, and the risk-weighted insurance demand or “loss coverage”. High fair-premium demand elasticity leads to a collapse in loss coverage, with an equilibrium premium close to the risk of the higher-risk population. Low fair-premium demand elasticity leads to an equilibrium premium close to the risk of the lower-risk population, and high loss coverage – possibly higher than under more complete risk classification. The demand elasticity parameters which are required to generate a collapse in coverage in the model in this paper appear higher than the values for demand elasticity which have been estimated in several empirical studies of various insurance markets. This offers a possible explanation of why some insurance markets appear to operate reasonably well under community rating, without the collapse in coverage which insurance folklore suggests.

This paper examines the validity of some stylized statements that can be found in the actuarial literature about random effects models. Specifically, the actual meaning of the estimated parameters and the nature of the residual heterogeneity are discussed. A numerical illustration performed on a Belgian motor third party liability portfolio supports this discussion.

In nonlife insurance, actuaries usually resort to random effects to take unexplained heterogeneity into account (in the spirit of the Bühlmann-Straub model). This paper aims to study the kind of dependence induced by the introduction of correlated latent variables in the annual numbers of claims reported by policyholders. The effect of reporting claims on the a posteriori distribution of the random effects will be made precise. This will be done by establishing some stochastic monotonicity property of the a posteriori distribution with respect to the claims history.