Journal: Scandinavian Actuarial Journal

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Taylor & Francis

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0346-1238
1651-2030

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Publications 1 - 10 of 17
  • Machine learning in individual claims reserving
    Item type: Journal Article
    Wüthrich, Mario V. (2018)
    Scandinavian Actuarial Journal
  • Claims frequency modeling using telematics car driving data
    Item type: Journal Article
    Gao, Guangyuan; Meng, Shengwang; Wüthrich, Mario V. (2019)
    Scandinavian Actuarial Journal
  • Double chain ladder, claims development inflation and zero claims
    Item type: Journal Article
    Martínez-Miranda, María Dolores; Nielsen, Jens Perch; Verrall, Richard; et al. (2015)
    Scandinavian Actuarial Journal
  • Group cohesion under individual regulatory constraints
    Item type: Journal Article
    Coculescu, Delia; Delbaen, Freddy (2022)
    Scandinavian Actuarial Journal
    We consider a group consisting of N business units. We suppose there are regulatory constraints for each unit; more precisely, the net worth of each business unit is required to belong to a set of acceptable risks, assumed to be a convex cone. Because of these requirements, there are less incentives to operate under a group structure, as creating one single business unit, or altering the liability repartition among units, may allow to reduce the required capital. We analyse the possibilities for the group to benefit from a diversification effect and economise on the cost of capital. We define and study the risk measures that allow for any group to achieve the minimal capital, as if it were a single unit, without altering the liability of business units, and despite the individual admissibility constraints. We call these risk measures cohesive risk measures. In the commonotonic case, we show that they are tail expectations but calculated under a different probability.
  • What is fair? Proxy discrimination vs. demographic disparities in insurance pricing
    Item type: Journal Article
    Lindholm, Mathias; Richman, Ronald; Tsanakas, Andreas; et al. (2024)
    Scandinavian Actuarial Journal
    Discrimination and fairness are major concerns in algorithmic models. This is particularly true in insurance, where protected policyholder attributes are not allowed to be used for insurance pricing. Simply disregarding protected policyholder attributes is not an appropriate solution as this still allows for the possibility of inferring protected attributes from non-protected covariates, leading to the phenomenon of proxy discrimination. Although proxy discrimination is qualitatively different from the group fairness concepts discussed in the machine learning and actuarial literature, group fairness criteria have been proposed to control the impact of protected attributes on the calculation of insurance prices. The purpose of this paper is to discuss the relationship between direct and proxy discrimination in insurance and the most popular group fairness axioms. We provide a technical definition of proxy discrimination and derive incompatibility results, showing that avoiding proxy discrimination does not imply satisfying group fairness and vice versa. This shows that the two concepts are materially different. Furthermore, we discuss input data pre-processing and model post-processing methods that achieve group fairness in the sense of demographic parity. As these methods induce transformations that explicitly depend on policyholders' protected attributes, it becomes ambiguous whether direct and proxy discrimination is, in fact, avoided.
  • Valuation portfolio in non-life insurance
    Item type: Journal Article
    Buchwalder, Markus; Bühlmann, Hans; Merz, Michael; et al. (2007)
    Scandinavian Actuarial Journal
  • Approximation methods for piecewise deterministic Markov processes and their costs
    Item type: Journal Article
    Kritzer, Peter; Leobacher, Gunther; Szölgyenyi, Michaela; et al. (2019)
    Scandinavian Actuarial Journal
    In this paper, we analyse piecewise deterministic Markov processes (PDMPs), as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of PDMPs. There one is interested in computing certain quantities of interest such as the probability of ruin or the value of an insurance company. Instead of explicitly solving the related integro-(partial) differential equation (an approach which can only be used in few special cases), we adapt the problem in a manner that allows us to apply deterministic numerical integration algorithms such as quasi-Monte Carlo rules; this is in contrast to applying random integration algorithms such as Monte Carlo. To this end, we reformulate a general cost functional as a fixed point of a particular integral operator, which allows for iterative approximation of the functional. Furthermore, we introduce a smoothing technique which is applied to the integrands involved, in order to use error bounds for deterministic cubature rules. We prove a convergence result for our PDMPs approximation, which is of independent interest as it justifies phase-type approximations on the process level. We illustrate the smoothing technique for a risk-theoretic example, and compare deterministic and Monte Carlo integration.
  • Neural network embedding of the over-dispersed Poisson reserving model
    Item type: Journal Article
    Gabriell, Andrea; Richman, Ronald; Wüthrich, Mario V. (2020)
    Scandinavian Actuarial Journal
  • LocalGLMnet: interpretable deep learning for tabular data
    Item type: Journal Article
    Richman, Ronald; Wüthrich, Mario V. (2023)
    Scandinavian Actuarial Journal
    Deep learning models have gained great popularity in statistical modeling because they lead to very competitive regression models, often outperforming classical statistical models such as generalized linear models. The disadvantage of deep learning models is that their solutions are difficult to interpret and explain, and variable selection is not easily possible because deep learning models solve feature engineering and variable selection internally in a nontransparent way. Inspired by the appealing structure of generalized linear models, we propose a new network architecture that shares similar features as generalized linear models but provides superior predictive power benefiting from the art of representation learning. This new architecture allows for variable selection of tabular data and for interpretation of the calibrated deep learning model, in fact, our approach provides an additive decomposition that can be related to other model interpretability techniques.
  • Bounds on the estimation error in the chain ladder method
    Item type: Journal Article
    Wüthrich, Mario V.; Merz, Michael; Bühlmann, Hans (2008)
    Scandinavian Actuarial Journal
    Buchwalder et al. (2006) have illustrated that there are different approaches for the derivation of an estimate for the parameter estimation error in the distribution-free chain ladder reserving method. In this paper, we demonstrate that these approaches provide estimates that are close to each other for typical parameters. This is carried out by proving upper and lower bounds. © 2008 Taylor & Francis.
Publications 1 - 10 of 17