Background

This research will investigate methodologies for reserving that, instead of relying on aggregated loss data structured into triangles to project losses for each year, utilize the most granular level of available information. The research will build on the work done in “Triangle-free reserving - A non-traditional framework for estimating reserves and reserve uncertainty”, Parodi (2014), which presented a practical implementation of the “triangle-free reserving” framework. The idea of granular reserving has actually been around since the 1990s, although mostly in academic circles.

The idea behind this research is that traditional reserving methods use aggregate data because they were developed at a time when computing power was limited. However, using aggregated data results in information compression and ultimately loss of information that hinders an accurate estimation of the statistical distribution of projected outcomes — which is the aim of a reserving exercise. Furthermore, pricing is normally undertaken at a more granular level, and there is therefore a disconnect from pricing. Reserving measures the risk retrospectively, while pricing measures it prospectively — however, the risk is fundamentally the same.

The triangle-free framework uses a frequency/severity approach based on the collective risk model, similar to what is done in pricing. This framework has been established and is currently in use, for example in claim count development in pricing (Parodi, 2023), but many questions remain unresolved, of both a theoretical and a practical nature. This project aims to advance on these questions.

Objectives 

In more detail, the project aims to:

1.    Gain an understanding of the relationship of triangle-free reserving with the other granular reserving methods developed in academia, such as Antonio & Plat (2014) and Taylor (2019).

2.    Prove, using independent loss generation processes (Alvarado et al., 2018) and carrying on the work started in Glionna & Parodi (2018; 2020), that under reasonably weak assumptions: (a) triangle-based methods do not produce the true reserving distribution, even asymptotically; (b) that triangle-free reserving with minimal or no human interaction outperforms systematically triangle-based methods, across the board but especially when data is scarce.

3.    Delve deeper into the theoretical aspects of the methodology, addressing (among other things) the dependencies among the various variables, and the role of external factors.  

Fields of research / technical cooperation 

• Actuarial

   

Works cited

• Alvarado et al. (2018), Loss simulation model and documentation, CAS Loss Simulator 2.0, https://www.casact.org/research/lsmwp/index.cfm?fa=software
• Antonio, K. & Plat, R. (2014), Micro-level stochastic loss reserving for general insurance, Scandinavian Actuarial Journal, (7), 649-669
• Glionna, A. & Parodi, P. (2018), Triangle-free reserving vs triangle-based methods: An Empirical comparison based on control data, International Conference of Actuaries, Berlin
• Glionna, A. & Parodi, P. (2020), ASTIN Webinar: Triangle-free reserving. See related slides.
• Parodi, P. (2014), Triangle-free reserving - A non-traditional framework for estimating reserves and reserve uncertainty,
• British Actuarial Journal, March 2014. (Also on GIRO proceedings, 2012.)
• Parodi, P. (2023), Pricing in general insurance (Section 13.3), 2nd Edition, CRC Press
• Taylor, G. (2019) Loss Reserving Models: Granular and Machine Learning Forms, Risks 7, no. 3: 82