Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression

33 Pages Posted: 12 Feb 2014

See all articles by Alice Dong

Alice Dong

The University of Sydney - School of Mathematics and Statistics

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics

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

Date Written: February 11, 2014

Abstract

We develop quantile regression models in order to derive risk margin and to evaluate capital in non-life insurance applications. By utilizing the entire range of conditional quantile functions, especially higher quantile levels, we detail how quantile regression is capable of providing an accurate estimation of risk margin and an overview of implied capital based on the historical volatility of a general insurers loss portfolio. Two modelling frameworks are considered based around parametric and nonparametric quantile regression models which we develop specifically in this insurance setting.

In the parametric quantile regression framework, several models including the flexible generalized beta distribution family, asymmetric Laplace (AL) distribution and power Pareto distribution are considered under a Bayesian regression framework. The Bayesian posterior quantile regression models in each case are studied via Markov chain Monte Carlo (MCMC) sampling strategies.

In the nonparametric quantile regression framework, that we contrast to the parametric Bayesian models, we adopted an AL distribution as a proxy and together with the parametric AL model, we expressed the solution as a scale mixture of uniform distributions to facilitate implementation. The models are extended to adopt dynamic mean, variance and skewness and applied to analyze two real loss reserve data sets to perform inference and discuss interesting features of quantile regression for risk margin calculations.

Keywords: Asymmetric Laplace distribution, Bayesian inference, Markov chain Monte Carlo methods, Quantile regression, loss reserve, risk margin, central estimate

Suggested Citation

Dong, Alice and Chan, Jennifer and Peters, Gareth, Risk Margin Quantile Function via Parametric and Non-Parametric Bayesian Quantile Regression (February 11, 2014). Available at SSRN: https://ssrn.com/abstract=2394063 or http://dx.doi.org/10.2139/ssrn.2394063

Alice Dong

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

Jennifer Chan

The University of Sydney - School of Mathematics and Statistics ( email )

Sydney, New South Wales 2006
Australia

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

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