Stochastic loss reserving with dependence: A flexible multivariate Tweedie approach

Abstract

Stochastic loss reserving with dependence has received increased attention in the last decade. A number of parametric multivariate approaches have been developed to capture dependence between lines of business within an insurer's portfolio. Motivated by the richness of the Tweedie family of distributions, we propose a multivariate Tweedie approach to capture cell-wise dependence in loss reserving. This approach provides a transparent introduction of dependence through a common shock structure. In addition, it also has a number of ideal properties, including marginal flexibility, transparency, and tractability including moments that can be obtained in closed form. Theoretical results are illustrated using both simulated data sets and a real data set from a property-casualty insurer in the US.

Common Shock Models for Claim Arrays

“…The member of (3.20) involving the α coefficient creates dependency between individual cells in the same location of different arrays. This case can be found in Braun (2004) and Avanzi, Taylor, Vu, and Wong (2016a).…”

“…diagonal) declines as the distance between diagonals increases; -formulate these dependencies in such a manner as to restrict the number of parameters involved, and therefore requiring estimation. A generalisation of common shock models (e.g., Meyers, 2007;Wüthrich and Merz, 2015;Avanzi, Taylor, Vu, and Wong, 2016a) is used to achieve these objectives. Our paper generalises Wüthrich and Merz (2015, e.g.…”

“…The common shock model was adapted to claim triangles in some papers such as De Jong (2006 or Avanzi, Taylor, Vu, and Wong (2016a). In its most basic form, the model for two variates A, B, subject to common shock, is as follows :…”

Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model

“…Based on MM-estimators, Peremans et al (2018) proposed a robust alternative that estimates the SUR parameters in a more outlier resistant way. Avanzi et al (2016aAvanzi et al ( , 2016b proposed a multivariate Tweedie approach to capture cell-wise dependence and the dependency between business segments in the non-life insurance industry, respectively, in loss reserving. In addition, Avanzi et al (2018) constructed a broad and flexible family of models, where dependency is induced by common shock components.…”

Modelling Outstanding Claims with Mixed Compound Processes in Insurance

“…Further generalization of GLMs in loss reserving exploits the richness of the Tweedie family of distributions (see Peters et al (2009); Wüthrich (2003)). For extensions to a flexible multivariate approach to consider the dependence between claims of different lines of business (LoBs) see Avanzi et al (2016). Other deterministic methods, such as Bornhuetter-Ferguson, have been recently integrated with a stochastic structure based on a Bayesian approach (England and Verrall, 2006;England et al, 2012), aiming at measuring the prediction error of the reserve estimate (Alai et al, 2009;Saluz et al, 2011).…”