Analytical and simulation-based approaches for quantifying multi-year risk in non-life insurance

Analytical and simulation-based approaches for quantifying multi-year risk in non-life insurance

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Projection of own funds and capital requirements over a multi-year horizon has become a fundamental component in modern risk- and value-based business planning and regulatory requirements for insurance companies.

The presentation provides an overview about the research work in the area of multi-year non-life insurance risk over the past six years. First, we recap the framework for multi-year risk quantification in non-life insurance business by defining m-year risk as the uncertainty w.r.t changes in basic own funds over the next m future calendar years.

Defining the m-year claims development result (CDR) as the underlying variable at risk, we present analytical closed-form formulae for the mean squared error of prediction of a single portfolio’s CDR under the assumption of the distribution-free chain ladder loss reserving models and additive reserving models, respectively. These analytic formulae are extended to multivariate versions for several lines of business, as demonstrated for the bivariate Chain-Ladder model (“Braun model”).

As an alternative and amendment to the analytical approaches we present a bootstrap approach using stochastic re-reserving to simulate a full predictive distribution for the aggregated CDR in the multivariate case of several loss portfolios combining the chain ladder loss reserving model and the additive reserving model.

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