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

53 Pages Posted: 3 May 2017

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Rodrigo Targino

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: May 2, 2017

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 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.

Keywords: Capital Allocation, Premium and Reserve Risk, Solvency Capital Requirement (SCR), Sequential Monte Carlo (SMC), Swiss Solvency Test (SST)

Suggested Citation

Peters, Gareth and Targino, Rodrigo and Wuthrich, Mario V., Bayesian Modelling, Monte Carlo Sampling and Capital Allocation of Insurance Risks (May 2, 2017). Available at SSRN: https://ssrn.com/abstract=2961888 or http://dx.doi.org/10.2139/ssrn.2961888

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Rodrigo Targino

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics ( email )

Praia de Botafogo
Rio de Janeiro, 22250-900
Brazil

HOME PAGE: http://https://sites.google.com/site/rodrigodossantostargino/

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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