Property graphs: A statistical model for fire losses based on graph theory

Property graphs: A statistical model for fire losses based on graph theory

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Speaker(s): Pietro Parodi (SCOR), Peter Watson (Cass Business School)

Severity loss amount distributions can rarely be derived from first principles. One such example is the use of generalized Pareto distribution for losses above a large threshold, which is dictated by extreme value theory. Most popular distributions, such as the lognormal distribution or the 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 (in the sense of graph theory), i.e. a collection of vertices and weighted edges connecting these vertices. Each vertex (which can also be weighted) corresponds to a room or a unit of the property where a fire can occur, while an edge (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 a simple model for fire propagation that allows to calculate the loss distribution for a given property from first principles. The characteristics of the loss distributions as a function of the number of "rooms" (a generic term for the basic unit of a property - but it could be a piece of machinery), of the connectivity of the graph (the average number of rooms communicating with another room), the average path length between two vertices of the graph, the probability of fire propagation between two vertices/rooms.

The relationship of this loss distribution to the classic MBBEFD framework is studied, showing that the full MBBEFD model is a good approximation for the empirical distribution of losses on a random graphs in many cases.

This methodology can be used as a basis for selecting the parameters that should be used for modelling a specific type of property (even of a type previously "off the charts").

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