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Stochastic models and methods for the assessment of earthquake risk in insurance

Jiménez-Huerta, Diego (2009) Stochastic models and methods for the assessment of earthquake risk in insurance. PhD thesis, The London School of Economics and Political Science (LSE).

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The problem of earthquake risk assessment and management in insurance is a challenging one at the interface of geophysics, engineering seismology, stochastics, insurance mathematics and economics. In this work, I propose stochastic models and methods for the assessment of earthquake risk from an insurer's point of view, where the aim is not to address problems in the financial mathematics and economics of risk selection, pricing, portfolio management, and risk transfer strategies such as reinsurance and securitisation, but to enable the latter through the characterisation of the foundation of any risk management consideration in insurance: the distribution of losses over a period of time for a portfolio of risks. Insurance losses are assumed to be generated by a loss process that is in turn governed by an earthquake process, a point process marked with the earthquake's hypocentre and magnitude, and a conditional loss distribution for an insurance portfolio, governing the loss size given the hypocentre and magnitude of the earthquake, and the physical characteristics of the portfolio as described in the individual policy records. From the modeling perspective, I examine the (non-trivial) minutiae around the infrastructure underpinning the loss process. A novel model of the earthquake process, a Poisson marked point process with spatial gamma intensity measure on the hypocentral space, and extensions of the Poisson and stress release models through the inclusion of hypocentral location in the mark, are proposed. I discuss the general architectural considerations for constructing the conditional loss distribution, and propose a new model as an alternative to the traditional ground motion attenuation and seismic vulnerability approach in engineering risk assessment. On the actuarial mathematics front, given a fully specified loss process, I address the problem of constructing simulation based and, where possible, analytical approximations to the distribution of portfolio losses over a period of time. I illustrate the applicability of the stochastic models and methods proposed in this work through the analysis of a residential homeowners property catastrophe portfolio exposed to earthquake risk in California. I construct approximations to the distribution of portfolio losses over a period of time under each of the three models of the earthquake process that I propose, and discuss their relative merits.

Item Type: Thesis (PhD)
Additional Information: © 2009 Diego Jiménez-Huerta
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Departments > Statistics
Supervisor: Norberg, Ragnar

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