Actuarial applications and estimation of extended CreditRisk⁺

Jonas Hirz, Uwe Schmock, P.V. Shevchenko

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
29 Downloads (Pure)


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 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.
Original languageEnglish
Article number23
Pages (from-to)1-29
Number of pages29
Issue number2
Publication statusPublished - Jun 2017


  • stochastic mortality model
  • extended CreditRisk+
  • risk aggregation
  • partial internal model
  • mortality risk
  • longevity risk
  • Markov chain Monte Carlo


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