Chain Ladder Method: Bayesian Bootstrap Versus Classical Bootstrap

37 Pages Posted: 5 Jun 2017

See all articles by Gareth Peters

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Mario V. Wuthrich

RiskLab, ETH Zurich

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics

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)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Mario V. Wuthrich

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics ( email )

Australia

HOME PAGE: http://www.mq.edu.au/research/centre-for-risk-analytics/pavel-shevchenko

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