ASTIN Bulletin

Journal Information
ISSN / EISSN : 0515-0361 / 1783-1350
Published by: Cambridge University Press (CUP) (10.1017)
Total articles ≅ 1,350
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, , , M.V. Wüthrich
Published: 7 October 2021
ASTIN Bulletin pp 1-35;

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.
Alexandre Corradin, Michel Denuit, Marcin Detyniecki, Vincent Grari, Matteo Sammarco,
Published: 7 October 2021
ASTIN Bulletin pp 1-22;

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.
Published: 4 October 2021
ASTIN Bulletin pp 1-31;

Spatial data are a rich source of information for actuarial applications: knowledge of a risk’s location could improve an insurance company’s ratemaking, reserving or risk management processes. Relying on historical geolocated loss data is problematic for areas where it is limited or unavailable. In this paper, we construct spatial embeddings within a complex convolutional neural network representation model using external census data and use them as inputs to a simple predictive model. Compared to spatial interpolation models, our approach leads to smaller predictive bias and reduced variance in most situations. This method also enables us to generate rates in territories with no historical experience.
Published: 31 August 2021
ASTIN Bulletin, Volume 51, pp 719-751;

Using telematics technology, insurers are able to capture a wide range of data to better decode driver behavior, such as distance traveled and how drivers brake, accelerate, or make turns. Such additional information also helps insurers improve risk assessments for usage-based insurance, a recent industry innovation. In this article, we explore the integration of telematics information into a classification model to determine driver heterogeneity. For motor insurance during a policy year, we typically observe a large proportion of drivers with zero accidents, a lower proportion with exactly one accident, and a far lower proportion with two or more accidents. We here introduce a cost-sensitive multi-class adaptive boosting (AdaBoost) algorithm we call SAMME.C2 to handle such class imbalances. We calibrate the algorithm using empirical data collected from a telematics program in Canada and demonstrate an improved assessment of driving behavior using telematics compared with traditional risk variables. Using suitable performance metrics, we show that our algorithm outperforms other learning models designed to handle class imbalances.
Published: 18 August 2021
ASTIN Bulletin, Volume 51, pp 779-812;

This article proposes a complex economic scenario generator that nests versions of well-known actuarial frameworks. The generator estimation relies on the Bayesian paradigm and accounts for both model and parameter uncertainty via Markov chain Monte Carlo methods. So, to the question is less more?, we answer maybe, but it depends on your criteria. From an in-sample fit perspective, on the one hand, a complex economic scenario generator seems better. From the conservatism, forecasting and coverage perspectives, on the other hand, the situation is less clear: having more complex models for the short rate, term structure and stock index returns is clearly beneficial. However, that is not the case for inflation and the dividend yield.
ASTIN Bulletin, Volume 51, pp 813-837;

In the context of the Solvency II directive, the operation of an internal risk model is a possible way for risk assessment and for the determination of the solvency capital requirement of an insurance company in the European Union. A Monte Carlo procedure is customary to generate a model output. To be compliant with the directive, validation of the internal risk model is conducted on the basis of the model output. For this purpose, we suggest a new test for checking whether there is a significant change in the modeled solvency capital requirement. Asymptotic properties of the test statistic are investigated and a bootstrap approximation is justified. A simulation study investigates the performance of the test in the finite sample case and confirms the theoretical results. The internal risk model and the application of the test is illustrated in a simplified example. The method has more general usage for inference of a broad class of law-invariant and coherent risk measures on the basis of a paired sample.
ASTIN Bulletin, Volume 51, pp 873-904;

Target benefit (TB) plans that incorporate intergenerational risk sharing have been demonstrated to be welfare improving over the long term. However, there has been little discussion of the short-term benefits for members in a defined benefit (DB) plan that is transitioning to TB. In this paper, we adopt a two-step approach that is designed to ensure the long-term sustainability of the new plan, without unduly sacrificing the benefit security of current retirees. We propose a cohort-based transition plan for reducing intergenerational inequity. Our study is based on simulations using an economic scenario generator with some theoretical results under simplified settings.
ASTIN Bulletin, Volume 51, pp 905-938;

We extend the Annually Recalculated Virtual Annuity (ARVA) spending rule for retirement savings decumulation (Waring and Siegel (2015) Financial Analysts Journal, 71(1), 91–107) to include a cap and a floor on withdrawals. With a minimum withdrawal constraint, the ARVA strategy runs the risk of depleting the investment portfolio. We determine the dynamic asset allocation strategy which maximizes a weighted combination of expected total withdrawals (EW) and expected shortfall (ES), defined as the average of the worst 5% of the outcomes of real terminal wealth. We compare the performance of our dynamic strategy to simpler alternatives which maintain constant asset allocation weights over time accompanied by either our same modified ARVA spending rule or withdrawals that are constant over time in real terms. Tests are carried out using both a parametric model of historical asset returns as well as bootstrap resampling of historical data. Consistent with previous literature that has used different measures of reward and risk than EW and ES, we find that allowing some variability in withdrawals leads to large improvements in efficiency. However, unlike the prior literature, we also demonstrate that further significant enhancements are possible through incorporating a dynamic asset allocation strategy rather than simply keeping asset allocation weights constant throughout retirement.
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