Replicating and extending chain-ladder via an age-period-cohort structure on the claim development in a run-off triangle

This paper introduces yet another stochastic model replicating chain-ladder estimates and furthermore considers extensions that add flexibility to the modeling. In its simplest form, the proposed model replicates the chain-ladder's development factors using a GLM model with averaged hazard rates running in reversed development time as response. This is in contrast to the existing reserving literature within the GLM framework where claim amounts are modeled as response. Modeling the averaged hazard rate corresponds to modeling the claim development and is arguably closer to the actual chain-ladder algorithm. Furthermore, since exposure does not need to be modeled, the model only has half the number of parameters compared to when modeling the claim amounts. This lesser complexity can be used to easily introduce model extensions that may better fit the data. We provide a new R-package, $\texttt{clmplus}$, where the models are implemented and can be fed with run-off triangles. We conduct an empirical study on 30 publicly available run-off triangles making a case for the benefit of having $\texttt{clmplus}$ in the actuary's toolbox

Identifiability and estimation of the competing risks model under exclusion restrictions

The non-identifiability of the competing risks model requires researchers to work with restrictions on the model to obtain informative results. We present a new identifiability solution based on an exclusion restriction. Many areas of applied research use methods that rely on exclusion restrcitions. It appears natural to also use them for the identifiability of competing risks models. By imposing the exclusion restriction couple with an Archimedean copula, we are able to avoid any parametric restriction on the marginal distributions. We introduce a semiparametric estimation approach for the nonparametric marginals and the parametric copula. Our simulation results demonstrate the usefulness of the suggested model, as the degree of risk dependence can be estimated without parametric restrictions on the marginal distributions

Hidden variables unseen by Random Forests

Random Forests are widely claimed to capture interactions well. However, some simple examples suggest that they perform poorly in the presence of certain pure interactions that the conventional CART criterion struggles to capture during tree construction. We argue that alternative partitioning schemes can enhance identification of these interactions. Furthermore, we extend recent theory of Random Forests based on the notion of impurity decrease by considering probabilistic impurity decrease conditions. Within this framework, consistency of a new algorithm coined 'Random Split Random Forest' tailored to address function classes involving pure interactions is established. In a simulation study, we validate that the modifications considered enhance the model's fitting ability in scenarios where pure interactions play a crucial role

Fairness: plurality, causality, and insurability

This article summarizes the main topics, findings, and avenues for future work from the workshop Fairness with a view towards insurance held August 2023 in Copenhagen, Denmark

Smooth backfitting of proportional hazards with multiplicative components

Smooth backfitting has proven to have a number of theoretical and practical advantages in structured regression. By projecting the data down onto the structured space of interest smooth backfitting provides a direct link between data and estimator. This paper introduces the ideas of smooth backfitting to survival analysis in a proportional hazard model, where we assume an underlying conditional hazard with multiplicative components. We develop asymptotic theory for the estimator. In a comprehensive simulation study we show that our smooth backfitting estimator successfully circumvents the curse of dimensionality and outperforms existing estimators. This is especially the case in difficult situations like high number of covariates and/or high correlation between the covariates, where other estimators tend to break down. We use the smooth backfitter in a practical application where we extend recent advances of in-sample forecasting methodology by allowing more information to be incorporated while still obeying the structured requirements of in-sample forecasting

Communication and personal selection of pension saver's financial risk

The paper shows how to reform the platform of pension products so that pension savers, professional financial advisors, actuaries and investment experts intuitively understand the underlying financial risk of the optimal investment profile. It is also pointed out that an excellent optimal investment strategy can destroy the future expected utility of a pension saver if the financial communication is wrong. It is shown that a simple system with an upper and a lower bound, originally inspired by Merton (2014), which can be executed easily using fintech, can replace complicated power utility optimization for the pension saver so that everyone can exactly understand the amount of financial risk taken. The paper focuses on investing money as a lump sum because being able to communicate the associated financial risk can serve as the first step towards communicating more complex pension saving structures

Random Planted Forest: a directly interpretable tree ensemble

We introduce a novel interpretable and tree-based algorithm for prediction in a regression setting in which each tree in a classical random forest is replaced by a family of planted trees that grow simultaneously. The motivation for our algorithm is to estimate the unknown regression function from a functional ANOVA decomposition perspective, where each tree corresponds to a function within that decomposition. Therefore, planted trees are limited in the number of interaction terms. The maximal order of approximation in the ANOVA decomposition can be specified or left unlimited. If a first order approximation is chosen, the result is an additive model. In the other extreme case, if the order of approximation is not limited, the resulting model puts no restrictions on the form of the regression function. In a simulation study we find encouraging prediction and visualisation properties of our random planted forest method. We also develop theory for an idealised version of random planted forests in the case of an underlying additive model. We show that in the additive case, the idealised version achieves up to a logarithmic factor asymptotically optimal one-dimensional convergence rates of order $n^{-2/5}$

Global Polynomial Kernel Hazard Estimation

This paper introduces a new bias reducing method for kernel hazard estimation. The method is called global polynomial adjustment (GPA). It is a global correction which is applicable to any kernel hazard estimator. The estimator works well from a theoretical point of view as it asymptotically reduces bias with unchanged variance. A simulation study investigates the finite-sample properties of GPA. The method is tested on local constant and local linear estimators. From the simulation experiment we conclude that the global estimator improves the goodness-of-fit. An especially encouraging result is that the bias-correction works well for small samples, where traditional bias reduction methods have a tendency to fail.En este artículo se introduce un nuevo método de correción del sesgo para la estimación núcleo de la función de riesgo. El método, denominado ajuste polinomial global (APG), consiste en una corrección global que es aplicable a cualquier tipo de estimador núcleo de la función de riesgo. Se comprueba que APG posee buenas propiedades asintóticas y que consigue reducir el sesgo sin incrementar la varianza. Se realizan estudios de simulación para evaluar las propiedades del APG en muestras finitas. Dichos estudios muestran un buen comportamiento en la práctica del APG. Esto es especialmente alentador dado que para muestras finitas los métodos tradicionales de reducción del sesgo tienden a tener un comportamiento bastante pobre