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PROPERTY GRAPHS – A STATISTICAL MODEL FOR FIRE AND EXPLOSION LOSSES BASED ON GRAPH THEORY

Published online by Cambridge University Press:  27 March 2019

Pietro Parodi  and
Peter Watson
Pietro Parodi*
Affiliation:
SCOR Global P&C London, UK E-Mail: pparodi@scor.com
Peter Watson
Affiliation:
SCOR Global P&C London, UK E-Mail: pwatson@scor.com
*
E-Mail: pparodi@scor.com
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Abstract

It is rare that the severity loss distribution for a specific line of business can be derived from first principles. One such example is the use of generalised Pareto distribution for losses above a large threshold (or more accurately: asymptotically), which is dictated by extreme value theory. Most popular distributions, such as the lognormal distribution or the Maxwell-Boltzmann-Bose-Einstein-Fermi-Dirac (MBBEFD), are convenient heuristics with no underlying theory to back them. This paper presents a way to derive a severity distribution for property losses based on modelling a property as a weighted graph, that is, a collection of nodes and weighted arcs connecting these nodes. Each node v (to which a value can also be assigned) corresponds to a room or a unit of the property where a fire can occur, while an arc (v, v′; p) between vertices v and v′ signals that the probability of the fire propagating from v to v′ is p. The paper presents two simple models for fire propagation (the random graph approach and the random time approach) and a model for explosion risk that allow one to calculate the loss distribution for a given property from first principles. The MBBEFD model is shown to be a good approximation for the simulated distribution of losses based on property graphs for both the random graph and the random time approach.

Keywords

Random graphexposure curveMBBEFDcritical threshold
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 263 - 297
Copyright
Copyright © Astin Bulletin 2019 

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