Linking Pensions to Life Expectancy: Tackling Conceptual Uncertainty through Bayesian Model Averaging

Linking pensions to longevity developments at retirement age has been one of the most common policy responses to pension schemes and aging populations. The introduction of automatic stabilizers is primarily motivated by cost containment objectives, but there are other dimensions of welfare restructuring in the politics of pension reforms, including recalibration, rationalization, and blame avoidance for unpopular policies that involve retrenchments. This paper examines the policy designs and implications of linking entry pensions to life expectancy developments through sustainability factors or life expectancy coefficients in Finland, Portugal, and Spain. To address conceptual and specification uncertainty in policymaking, we propose and apply a Bayesian model averaging approach to stochastic mortality modeling and life expectancy computation. The results show that: (i) sustainability factors will generate substantial pension entitlement reductions in the three countries analyzed; (ii) the magnitude of the pension losses depends on the factor design; (iii) to offset pension cuts and safeguard pension adequacy, individuals will have to prolong their working lives significantly; (iv) factor designs considering cohort longevity markers would have generated higher pension cuts in countries with increasing life expectancy gap.

POINT AND INTERVAL FORECASTS OF DEATH RATES USING NEURAL NETWORKS

The Lee–Carter model has become a benchmark in stochastic mortality modeling. However, its forecasting performance can be significantly improved upon by modern machine learning techniques. We propose a convolutional neural network (NN) architecture for mortality rate forecasting, empirically compare this model as well as other NN models to the Lee–Carter model and find that lower forecast errors are achievable for many countries in the Human Mortality Database. We provide details on the errors and forecasts of our model to make it more understandable and, thus, more trustworthy. As NN by default only yield point estimates, previous works applying them to mortality modeling have not investigated prediction uncertainty. We address this gap in the literature by implementing a bootstrapping-based technique and demonstrate that it yields highly reliable prediction intervals for our NN model.

Designing Annuities with Flexibility Opportunities in an Uncertain Mortality Scenario

We consider annuity designs in which the benefit amount is allowed to fluctuate (up or down), based on a given mortality/longevity experience. This way, guarantees are relaxed in respect of traditional annuity arrangements. On the other hand, while the annuitant is exposed to the risk of a future reduction of the benefit amount because of higher longevity, he/she can immediately take advantage of a lower premium loading, as well as of a future increase of the benefit amount in the case of higher mortality. Flexibility in the annuity design could be welcomed by individuals, as the conservative features of traditional products partly explain their lack of attractiveness in most markets. To further contribute to the flexibility of the product, we suggest a pricing structure based on periodic fees applied to the policy fund, instead of the usual upfront loading at issue. Periodic fees are more suitable to support a revision of the arrangement after issue, which is currently not allowed in traditional annuity products. We show that periodic fees can be introduced by identifying a discount factor to be used for pricing and reserving. We assume stochastic mortality, and we compare alternative mortality/longevity linking solutions, by assessing the periodic fees and other quantities.

A Square-Root Factor-Based Multi-Population Extension of the Mortality Laws

In this paper, we present and calibrate a multi-population stochastic mortality model based on latent square-root affine factors of the Cox-Ingersoll and Ross type. The model considers a generalization of the traditional actuarial mortality laws to a stochastic, multi-population and time-varying setting. We calibrate the model to fit the mortality dynamics of UK males and females over the last 50 years. We estimate the optimal states and model parameters using quasi-maximum likelihood techniques.

Combining Investment and Tax Strategies for Optimizing Lifetime Solvency under Uncertain Returns and Mortality

This paper considers investors who are looking to maximize their probability of remaining solvent throughout their lifetime by using an algorithm that aims to optimize their investment allocation strategy and optimize their tax strategy for withdrawal allocations between tax deferred accounts (TDAs), Roth accounts, and taxable stock and bond accounts. This optimization works with stochastic investment returns and stochastic mortality, extending and combining different investment and tax-efficiency paradigms. We find that optimizing the investment strategy has a much larger impact on the investor remaining solvent than optimizing the tax strategy. This result is key to effectively optimizing both strategies simultaneously. This optimized investment strategy soundly beats a standard target date fund strategy, and the novel optimized tax strategy displays optimal desired properties suggested by non-stochastic tax optimization research.

Spawning strategies in cypriniform fishes in a lowland river invaded by non-indigenous European barbel Barbus barbus

Spawning strategies of lowland river fishes include single spawning, where reproduction generally occurs in early spring to provide 0+ fish with an extended growth season through the summer, but with a high risk of stochastic mortality events occurring, such as early summer floods. This risk can be reduced by multiple or protracted spawning strategies, where 0+ fish are produced over an extended period, often into mid-summer, but with the trade-off being a shorter growth season. The spawning strategies of cypriniform fish were explored in the River Teme, a spate river in Western England, which has non-indigenous European barbel Barbus barbus present. Sampling 0+ fish in spring and summer and across three spawning periods, B. barbus, chub Squalius cephalus and minnow Phoxinus phoxinus always revealed multiple spawning events, with 0+ fish of < 20 mm present in samples collected from June to August. Fish below 20 mm in August remained relatively small by the end of their growth season (October). For dace Leuciscus leuciscus, only single spawning events were evident, but with 0+ dace always being relatively large. Therefore, multiple spawning appears to be a common strategy that provides resilience in 0+ fish against stochastic mortality events in lowland rivers.