Model risk in claims reserving within Tweedie's compound Poisson - - PowerPoint PPT Presentation

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Model risk in claims reserving within Tweedie's compound Poisson - - PowerPoint PPT Presentation

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Model risk in claims reserving within Tweedie's compound Poisson models Dr Pavel V. Shevchenko Principal Research Scientist, Team leader CSIRO Division of Mathematical and Information Sciences Quantitative Risk Management group, Sydney,

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Model risk in claims reserving within Tweedie's compound Poisson models

Dr Pavel V. Shevchenko Principal Research Scientist, Team leader CSIRO Division of Mathematical and Information Sciences Quantitative Risk Management group, Sydney, Australia

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  • mail:

mail: Pavel.Shevchenko@csiro.au Pavel.Shevchenko@csiro.au www.cmis.csiro.au/Pavel.Shevchenko www.cmis.csiro.au/Pavel.Shevchenko

Gareth Peters (UNSW/CSIRO), Pavel Shevchenko (CSIRO), and Mario Wüthrich (ETH). Model risk in claims reserving within Tweedie's compound Poisson models, preprint 2008. ASTIN Colloquium, Manchester, UK, July 2008 ASTIN Colloquium, Manchester, UK, July 2008

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Commonwealth Scientific and Industrial Research Organization of Australia (CSIRO) – national research agency formed in 1926. Approx 6500 staff (Divisions: Industrial

Physics, Minerals, Mathematical&Information Sciences, Marine and Atmospheric Research, etc.) www.csiro.au

Division of Mathematical and Information Sciences (CMIS)

(over 100 researchers): Decision Technology, Biotechnology and Health Informatics, Environmental Informatics www.cmis.csiro.au

Quantitative Risk Management (QRM) group (approx. 20

staff): financial risk, infrastructure, environment risk, security, air- transport). Financial Risk – operational risk, credit risk, market risk,

  • ption pricing, insurance – validation, consulting, model and software

development, www.cmis.csiro.au/QRM

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Claims Reserving (non-life insurance), solvency requirements, claims development triangle (real data)

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Content

Tweedie’s compound Poisson family to model annual

claims

Process Uncertainty, Parameter Estimation Error, Model

uncertainty

Variable selection Maximum likelihood and Bayesian estimation MCMC (random walk Metropolis-Hastings within Gibbs) Analysis/Conclusions

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  • predictor for and estimator for

Mean Square Error

  • f Prediction

“best estimate” of reserve

Bayesian context – variance decomposition

is model parameter vector modelled as random variable

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Tweedie’s compound Poisson model

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Tweedie’s compound Poisson: exponential dispersion family representation

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Tweedie’s compound Poisson model: final representation

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Parameter estimation: Model assumptions:

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Likelihood function

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Maximum likelihood: process and estimation errors

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Bayesian inference

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Bayesian inference estimates

Note, model error is incorporated via averaging over values of p

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Random Walk Metropolis Hastings (RW-MH) within Gibbs

Note: normalization constant in posterior is not needed;

  • ptimal acceptance rate is 0.234
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Full predictive distribution

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Variable selection models

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Variable selection models

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Variable selection models

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Claims reserves

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Results: average over p Results: conditioning on p

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Conclusions

Development of a Bayesian model for claims reserving

under Tweedie’s compound Poisson model covering range between Poisson and Gamma models

Quantification process, estimation and model

uncertainties and variable selection using MCMC (random walk Metropolis-Hastings within Gibbs)

MLEs are materially different from Bayesian

estimators – posterior distributions are different from Gaussian. Future work: variable selection problem – Reversible Jump MCMC; considering model parameter p outside the (1, 2) range; dynamic model.

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Thank you

Pavel Shevchenko Principal Research Scientist CSIRO Mathematical & Information Sciences Email: Pavel.Shevchenko@csiro.au www.cmis.csiro.au/Pavel.Shevchenko