Speakers: Lukas Hahn, Marc Linde
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. For example, the Own Risk and Solvency Assessment (ORSA) process under Solvency II requires forecasting of the Overall Solvency Needs, i.e. the capital requirements based on the undertaking-specific risk profile, tolerance, and business plans, especially when the assumptions for the Solvency Capital Requirement (SCR) of the Solvency II standard formula are violated.
We apply stochastic re-reserving based on underlying non-parametric and parametric bootstrap models to simulate the full predictive distribution of the undertaking-specific multi-year technical result of a non-life insurance company. The models are flexible to deal with an arbitrary number of possibly dependent loss portfolios that meet the assumptions of either the classical distribution-free chain-ladder model or the additive loss reserving model. Generalized versions of these reserving models with user-defined weighting of observations and mixtures of both models among the set of portfolios are possible. The full predictive distribution allows to quantify multi-year non-life insurance risk and its reserve and premium risk components through corresponding risk measures, e.g. the Value-at-Risk as in Solvency II, applied to the change in the basic own funds of the insurance company over a multi-year time horizon.
Based on data of a fictional non-life insurance company running multiple lines of business with different run-off behavior, we conduct an extensive and insightful case study in light of the ORSA process. In particular, we calculate the SCR according to our full undertaking-specific non-life insurance risk and benchmark it against the SCR for the non-life insurance risk module according to the Solvency II standard formula module. We further survey the performance of closed-form estimators for the mean squared error of prediction from recent analytic approaches.