Chain Ladder Method: Bayesian Bootstrap Versus Classical Bootstrap

37 Pages Posted: 5 Jun 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

Mario V. Wuthrich

RiskLab, ETH Zurich

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Date Written: 2009

Abstract

The intention of this paper is to analyse the mean square error of prediction (MSEP) under the distribution-free chain ladder (DFCL) claims reserving method. We compare the estimation obtained from the classical bootstrap method with the one obtained from a Bayesian bootstrap. To achieve this in the DFCL model we develop a novel approximate Bayesian computation (ABC) sampling algorithm to obtain the empirical posterior distribution. We need an ABC sampling algorithm because we work in a distribution-free setting. The use of this ABC methodology combined with bootstrap allows us to obtain samples from the intractable posterior distribution without the requirement of any distributional assumptions. This then enables us to calculate the MSEP and other risk measures like Value-at-Risk.

Keywords: claims reserving, distribution-free chain ladder, mean square error of prediction, Bayesian chain ladder, approximate Bayesian computation, Markov chain Monte Carlo, adaption, annealing, bootstrap

Suggested Citation

Peters, Gareth and Wuthrich, Mario V. and Shevchenko, Pavel V., Chain Ladder Method: Bayesian Bootstrap Versus Classical Bootstrap (2009). Available at SSRN: https://ssrn.com/abstract=2980411 or http://dx.doi.org/10.2139/ssrn.2980411

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

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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