Life Table Forecasting in COVID-19 Times: An Ensemble Learning Approach

Stochastic mortality modeling play a critical role in public pension design, population and public health projections and in the design, pricing and risk management of life insurance contracts and longevity-linked securities. There is no general method to forecast mortality rate applicable to all situations especially for unusual years such as the COVID-19 pandemic. In this paper, we investigate the feasibility of using an ensemble of traditional and machine learning time series methods to empower forecasts of age-specific mortality rates for groups of countries that share common longevity trends. We use Generalized Age-Period-Cohort stochastic mortality models to capture age and period effects, apply K-means clustering to time series to group countries following common longevity trends and use ensemble learning to forecast future longevity and annuity price markers. To calibrate models, we use data for 14 European countries from 1960 to 2018. The results show that the ensemble method presents the best robust results overall with minimum RMSE in the presence of structural changes in the shape of time series at the time of COVID-19.

“Allowing for shocks in portfolio mortality models” by Stephen Richards

Before founding Longevitas, Stephen headed the longevity analysis team at Prudential and prior to that he headed the product pricing team at Standard Life. [...]there is more to mortality shocks than just COVID-19. Nelson–Aalen estimators are simply the sum of the crude daily mortality rates on the days that at least once death occurs. \({\mathop {\hat{\Lambda }}olimits_{y,t}}\) estimates the integrated hazard over calendar time, which we illustrate with three international annuity portfolios: To get more detail, we calculate the first central difference for the Nelson–Aalen estimator around a point in time: \[{\hat \mu _{y + t}} = {{({{\hat \Lambda }_{_{y,t + {c \over 2}}}} - {{\hat \Lambda }_{y,t - {c \over 2}}}} \over c}\] where \(c\gt0\) is the bandwidth parameter. \({\mathop {\hat{\mu }}olimits_{{\text{y}} + {\text{t}}}}\) here is just the portfolio hazard estimate over time without any risk factors.

Special Issue “Quantitative Risk Assessment in Life, Health and Pension Insurance”

The high volatility in financial markets, together with the ultra-low interest rates environment and the increased expectation of life, constitute serious threats for providers of long-term investment guarantees and lifelong benefits. To this end, a stochastic model for traditional life insurance contracts is proposed and framed within the Solvency II Directive. The paper ends with the presentation of a case study of a portfolio of life insurance contracts, which testifies the effectiveness of the model in highlighting the main drivers of capital requirement evaluation.

Optimal Asset Allocation Subject to Withdrawal Risk and Solvency Constraints

This paper investigates the optimal asset allocation of a financial institution whose customers are free to withdraw their capital-guaranteed financial contracts at any time. In accounting for the asset-liability mismatch risk of the institution, we present a general utility optimization problem in a discrete-time setting and provide a dynamic programming principle for the optimal investment strategies. Furthermore, we consider an explicit context, including liquidity risk, interest rate, and credit intensity fluctuations, and show by numerical results that the optimal strategy improves both the solvency and asset returns of the institution compared to a standard institutional investor’s asset allocation.

Allowing for shocks in portfolio mortality models

The COVID-19 pandemic creates a challenge for actuaries analysing experience data that include mortality shocks. Without sufficient local flexibility in the time dimension, any analysis based on the most recent data will be biased by the temporarily higher mortality. Also, depending on where the shocks sit in the exposure period, any attempt to identify mortality trends will be distorted. We present a methodology for analysing portfolio mortality data that offer local flexibility in the time dimension. The approach permits the identification of seasonal variation, mortality shocks and occurred-but-not reported deaths (OBNR). The methodology also allows actuaries to measure portfolio-specific mortality improvements. Finally, the method assists actuaries in determining a representative mortality level for long-term applications like reserving and pricing, even in the presence of mortality shocks. Results are given for a mature annuity portfolio in the UK, which suggest that the Bayesian information criterion is better for actuarial model selection in this application than Akaike’s information criterion.

Unclaimed Defined Benefit Pensions Can Help COVID-19 Economic Recovery.

The COVID-19 economic crisis makes it vitally important that workers who earned defined benefit pensions receive them at retirement. Unfortunately, billions of dollars that could help cushion the financial shock are sitting unclaimed, because the people who they belong to cannot locate the company responsible for paying them. As defined benefit pension plans have been terminated, merged and moved over the years, large numbers of deferred vested participants have not been notified about their benefits. The widespread and growing practice of insurance company pension buy-outs can be especially problematic for participants without notice. Broader use of electronic disclosures for pensions also threatens to make the situation worse. In the wake of COVID-19, policy makers should take steps to ensure that pension benefits are part of the economic recovery.