European Actuarial Journal最新文献

A Neural Network (NN) approach for the modelling of mortality rates in a multi-population framework is compared to three classical mortality models. The NN setup contains two instances of Recurrent NNs, including Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU) networks. The stochastic approaches comprise the Li and Lee model, the Common Age Effect model of Kleinow, and the model of Plat. All models are applied and compared in a large case study on decades of data of the Italian population as divided in counties. In this case study, a new index of multiple deprivation is introduced and used to classify all Italian counties based on socio-economic indicators, sourced from the local office of national statistics (ISTAT). The aforementioned models are then used to model and predict mortality rates of groups of different socio-economic characteristics, sex, and age.

Participating life insurance contracts are policies that provide dividends (participation bonuses) based on the insurer’s financial performance. While these products are popular, there exists a gap in the literature for the analysis of these contracts under a stochastic setting. This paper fills this gap by proposing methods to (i) determine performance bonuses, (ii) compute the fair premium of the contract, and (iii) perform risk measurements for participating contracts in a realistic stochastic environment. The specific case of a fixed premium endowment participating contract, where the annual premium remains constant while benefits increase stochastically, is considered. We extend both the variable benefits life insurance approach of Bowers et al. [9] and the compound reversionary bonus mechanism presented in Booth et al. [8] and Bacinello [2] to a stochastic financial market (including stochastic interest rates) and stochastic mortality framework. Monte Carlo simulations provide insight about the sensitivity of premiums to contract specification and the evolution over time of both benefits and risks faced by the insurer.

Integrating epidemiological information into mortality models has the potential to improve forecasting accuracy and facilitate the assessment of preventive measures that reduce disease risk. While probabilistic models are often used for mortality forecasting, predicting how a system behaves under external manipulation requires a causal model. In this paper, we utilize the potential outcomes framework to explore how population-level mortality forecasts are affected by interventions, and discuss the assumptions and data needed to operationalize such an analysis. A unique challenge arises in population-level mortality models where common forecasting methods treat risk prevalence as an exogenous process. This approach simplifies the forecasting process but overlooks (part of) the interdependency between risk and death, limiting the model’s ability to capture selection-induced effects. Using techniques from causal mediation theory, we quantify the selection effect typically missing in studies on cause-of-death elimination and when analyzing actions that modify risk prevalence. Specifically, we decompose the total effect of an intervention into a part directly attributable to the intervention and a part due to subsequent selection. We illustrate the effects with U.S. data.

Abstract

We consider an empirical backtesting for the Solvency Capital Required (SCR) under Solvency II. Based on empirical facts that the Basic own Funds (BoF) can be assumed to evolve log-normally and have a much lower volatility than the corresponding equity for our test data, we make a proposal based on Earnings at Risk (EaR) that can be used to reduce the biases from overshooting SCR estimates in a prudential way.

COVID-19 has affected mortality rates and financial markets worldwide. Against this background, we perform a COVID-19 stress test for life insurance, considering a joint financial and mortality shock, to evaluate the effectiveness of different risk mitigation strategies. Specifically, we conduct a model-based simulation analysis of a life insurer selling annuities and term life insurances. The analysis includes stress scenarios that are calibrated to observations during the first year of the COVID-19 pandemic. We also consider new business and study the risk situation under three different risk mitigation strategies observed in practice as an immediate response to the pandemic: stopping sales, increasing premiums, or adjusting investment strategies. Results show that a life insurer’s risk situation is mainly affected in the short term, selling annuities (in addition to term life insurance) immunizes against the mortality shock, and the immediate use of risk mitigation strategies can help reduce the negative impact.