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Risks 2017, 5(4), 53; doi:10.3390/risks5040053

Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks

1
Department of Statistical Science, University College London, London WC1E 6BT, UK
2
Oxford-Man Institute, Oxford University, Oxford OX1 2JD, UK
3
System Risk Center, London School of Economics, London WC2A 2AE, UK
4
Fundação Getulio Vargas, Escola de Matemática Aplicada, Botafogo, RJ 22250-040, Brazil
5
RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
Received: 3 May 2017 / Revised: 30 August 2017 / Accepted: 31 August 2017 / Published: 22 September 2017
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Abstract

The main objective of this work is to develop a detailed step-by-step guide to the development and application of a new class of efficient Monte Carlo methods to solve practically important problems faced by insurers under the new solvency regulations. In particular, a novel Monte Carlo method to calculate capital allocations for a general insurance company is developed, with a focus on coherent capital allocation that is compliant with the Swiss Solvency Test. The data used is based on the balance sheet of a representative stylized company. For each line of business in that company, allocations are calculated for the one-year risk with dependencies based on correlations given by the Swiss Solvency Test. Two different approaches for dealing with parameter uncertainty are discussed and simulation algorithms based on (pseudo-marginal) Sequential Monte Carlo algorithms are described and their efficiency is analysed. View Full-Text
Keywords: capital allocation; premium and reserve risk; Solvency Capital Requirement (SCR); Sequential Monte Carlo (SMC); Swiss Solvency Test (SST) capital allocation; premium and reserve risk; Solvency Capital Requirement (SCR); Sequential Monte Carlo (SMC); Swiss Solvency Test (SST)
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Peters, G.W.; Targino, R.S.; Wüthrich, M.V. Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks. Risks 2017, 5, 53.

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