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Risks 2017, 5(2), 23; doi:10.3390/risks5020023

Actuarial Applications and Estimation of Extended CreditRisk+

1
BELTIOS GmbH, Lehargasse 1, Vienna 1060, Austria
2
Department of Financial and Actuarial Mathematics, TU Wien, Wiedner Hauptstr. 8–10, Vienna 1040, Austria
3
Department of Applied Finance and Actuarial Studies, Macquarie University, NSW 2109, Australia
*
Author to whom correspondence should be addressed.
Received: 20 January 2017 / Revised: 22 March 2017 / Accepted: 26 March 2017 / Published: 31 March 2017
(This article belongs to the Special Issue Ageing Population Risks)
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Abstract

We introduce an additive stochastic mortality model which allows joint modelling and forecasting of underlying death causes. Parameter families for mortality trends can be chosen freely. As model settings become high dimensional, Markov chain Monte Carlo (MCMC) is used for parameter estimation. We then link our proposed model to an extended version of the credit risk model CreditRisk+. This allows exact risk aggregation via an efficient numerically stable Panjer recursion algorithm and provides numerous applications in credit, life insurance and annuity portfolios to derive P&L distributions. Furthermore, the model allows exact (without Monte Carlo simulation error) calculation of risk measures and their sensitivities with respect to model parameters for P&L distributions such as value-at-risk and expected shortfall. Numerous examples, including an application to partial internal models under Solvency II, using Austrian and Australian data are shown. View Full-Text
Keywords: stochastic mortality model; extended CreditRisk+; risk aggregation; partial internal model; mortality risk; longevity risk; Markov chain Monte Carlo stochastic mortality model; extended CreditRisk+; risk aggregation; partial internal model; mortality risk; longevity risk; Markov chain Monte Carlo
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hirz, J.; Schmock, U.; Shevchenko, P.V. Actuarial Applications and Estimation of Extended CreditRisk+. Risks 2017, 5, 23.

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