Temporal clustering and renewal processes in empirical and modelled data

Temporal clustering and renewal processes in empirical and modelled data

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Speakers: Stefan Reimann, David Baumgartner

Temporal clustering of events is a well-documented phenomenon for natural disasters such as winter storms, earthquakes, or floods [1,2,3,4,8]. It constitutes a footprint for memory in the arrival process.
The reflection of temporal clustering poses a challenge for the assessment of aggregated risk in the context of both pricing and risk management [6]. In an independent single-event view, temporal clustering is often addressed by employing a Negative Binomial frequency distribution for the yearly loss aggregation. However, this modelling approach ignores the existence of memory in the process.

We propose a novel and general simulation method for the risk assessment of phenomena exhibiting temporal clustering. It is based on the theory of renewal-reward processes [7]: The reward function of the inter-arrival times is derived from the distribution of empirical inter-arrival times after adjusting for periodic patterns such as seasonality, El Nino or the Atlantic Multidecadeal Oscillation.

The model allows a quantitative analysis of the degree of clustering in event sequences. It can also be applied to climate models [5] as a test and diagnosis tool.

The application to risk assessment is based on constructing probabilistic sequences of arrival times for the event under consideration, which - in distribution - are identical to the empirical inter-arrival times. The so-modelled inter-arrival times provide the basis for the risk assessment in any probabilistic framework.

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