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Cited by 40Insurance, Mortality, Demography, Risk ManagementInsurance and Financial Risk ManagementStochastic processes and financial applications

Pricing Participating Longevity-Linked Life Annuities: A Bayesian Model Ensemble approach

Open access
Bravo, Jorge Miguel·2022·European Actuarial Journal
DOI 10.1007/s13385-021-00279-wPMC PMC8117133
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Abstract

Participating longevity-linked life annuities (PLLA) in which benefits are updated periodically based on the observed survival experience of a given underlying population and the performance of the investment portfolio are an alternative insurance product offering consumers individual longevity risk protection and the chance to profit from the upside potential of financial market developments. This paper builds on previous research on the design and pricing of PLLAs by considering a Bayesian Model Ensemble of single population generalised age-period-cohort stochastic mortality models in which individual forecasts are weighted by their posterior model probabilities. For the valuation, we adopt a longevity option decomposition approach with risk-neutral simulation and investigate the sensitivity of results to changes in the asset allocation by considering a more aggressive lifecycle strategy. We calibrate models using Taiwanese (mortality, yield curve and stock market) data from 1980 to 2019. The empirical results provide significant valuation and policy insights for the provision of a cost effective and efficient risk pooling mechanism that addresses the individual uncertainty of death, while providing appropriate retirement income and longevity protection.

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  • GLMs belittle conceptual uncertainty in empirical modelling.

    “Fourth, GLMs belittle conceptual uncertainty in empirical modelling, with recent literature highlighting the advantages of model ensembles in risk management (see, e.g., Bravo 2021).”

    From Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting (2023) · cites this paper as Bravo 2021

    The Conclusion (page not available in our copy) says a single-model framework misses sources of risk that a Bayesian model ensemble can capture, and that model combinations give a more realistic assessment of forecast uncertainty. It does not single out GLMs as belittling conceptual uncertainty, so the claim is broader and more specific about the model type than the source supports. (LLM, conf=0.84)

    Experimental — accuracy not yet measured

  • Ensemble models have a long tradition in the statistical and forecasting literature, yet they are relatively underexplored in insurance pricing.

    “They have a long tradition in the statistical and forecasting literature, yet they are relatively underexplored in insurance pricing (Bravo 2021).”

    From Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting (2023) · cites this paper as Bravo 2021

    The Materials and methods section describes ensemble learning as widely applied in forecasting, supporting the first part of the claim. It says mortality-rate forecasting has traditionally relied on a single model, but does not establish that ensembles are relatively underexplored across insurance pricing generally. No page number is available in our copy. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • Ensemble methods can provide superior predictive accuracy relative to single learners in several domain-specific areas.

    “Empirical studies show that they can provide superior predictive accuracy relative to single learners in several domain-specific areas (Ashofteh et al. 2022; Ayuso et al. 2021; Bravo 2021; Kim and Baek 2022).”

    From Modelling Motor Insurance Claim Frequency and Severity Using Gradient Boosting (2023) · cites this paper as Bravo 2021

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Authors
Bravo, J. M.
Affiliations
Universidade Nova de Lisboa (PT)
Corresponding author
Bravo, Jorge Miguel
ORCID
Bravo, Jorge Miguel
Venue
European Actuarial Journal
Publisher
Springer Science and Business Media LLC
Published
2021-05-13
Volume
12
Issue
1
Pages
125-159
ISSN
  • 2190-9733 (ISSN-L)
  • 2190-9741
DOI
10.1007/s13385-021-00279-w
PMC
PMC8117133
OpenAlex
W3162090594
Cited by
40
References
69
Citations by year
2026: 3 · 2025: 4 · 2024: 5 · 2023: 5 · 2022: 5 · 2021: 9 · 2020: 9
FWCI
9.45
Type
journal article
Language
en
Open access
Licence
Locations
  • European Actuarial Journal (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) (submittedVersion, other-oa)
Funders
Fundação para a Ciência e a Tecnologia (UIDB/04152/2020)
Topics
  • Social Sciences › Demography › Insurance, Mortality, Demography, Risk Management
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Insurance and Financial Risk Management
  • Social Sciences › Economics, Econometrics and Finance › Finance › Stochastic processes and financial applications
Keywords
stochastic mortality, asset allocation, retirement income

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