Heterogeneity in Survival Models - Applications to Pensions and Life Annuities

Olivieri, Annamaria

doi:10.2139/ssrn.913770

Cited by 23 publications

(25 citation statements)

References 46 publications

(58 reference statements)

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“…All of the results that are commented on in this section are well known. We then skip the details, which can be found in the references already provided; see, for example, [2,19] or [3].…”

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

“…We note that (13) is in the logistic class; such models imply a deceleration in the increasing age-pattern of mortality, which in the current setting is a consequence of the presence of frailty in the population. For a formal approach and more details, see, for example, [3,24].…”

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

“…In this paper, heterogeneity is addressed via a frailty model. For a short review of models accounting for observable risk factors, see, for example, [3,4], as well as the references therein. mainly focus on the design of a risk classification structure with respect to mortality (and we can exclude a correlation between financial and mortality risk).…”

Section: Introductionmentioning

confidence: 99%

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Frailty and Risk Classification for Life Annuity Portfolios

Olivieri

Pitacco

2016

Risks

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Life annuities are attractive mainly for healthy people. In order to expand their business, in recent years, some insurers have started offering higher annuity rates to those whose health conditions are critical. Life annuity portfolios are then supposed to become larger and more heterogeneous. With respect to the insurer's risk profile, there is a trade-off between portfolio size and heterogeneity that we intend to investigate. In performing this, there is a second and possibly more important issue that we address. In actuarial practice, the different mortality levels of the several risk classes are obtained by applying adjustment coefficients to population mortality rates. Such a choice is not supported by a rigorous model. On the other hand, the heterogeneity of a population with respect to mortality can formally be described with a frailty model. We suggest adopting a frailty model for risk classification. We identify risk groups (or classes) within the population by assigning specific ranges of values to the frailty within each group. The different levels of mortality of the various groups are based on the conditional probability distributions of the frailty. Annuity rates for each class then can be easily justified, and a comprehensive investigation of insurer's liabilities can be performed.

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“…All of the results that are commented on in this section are well known. We then skip the details, which can be found in the references already provided; see, for example, [2,19] or [3].…”

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

Section: Lifetime and Frailty: The Gompertz-gamma Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frailty and Risk Classification for Life Annuity Portfolios

Olivieri

Pitacco

2016

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“…[13,17] for details and references). In that context, the adjustment coefficient has been taken deterministic to represent heterogeneity originated by observable risk factors; conversely, heterogeneity due to unobservable risk factors has been represented by assuming a random coefficient (model (5) has been suggested, with reference to the force of mortality, by [23], where the coefficient Z x,t is named frailty).…”

Section: The Poisson-gamma Modelmentioning

confidence: 99%

“…In principle, Solvency 2 refers to a Value-atRisk assessment at a 99.5% confidence level with a one year time-horizon (for details, see [7]). So, in (19) we should set e ¼ 0:005: As far as the time-horizon is concerned, we must point out that (17) implies reference to the whole residual duration of the in-force portfolio, as a permanent shock is addressed. Reference to the whole residual duration clearly emerges in (18), as the reserve is the present value of all future outflows.…”

Section: Stochastic Approachmentioning

confidence: 99%

Stochastic mortality: experience-based modeling and application issues consistent with Solvency 2

Olivieri

2011

Eur. Actuar. J.

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This paper is motivated by the need to have appropriate tools for the valuation of mortality/longevity risks when carrying out an internal assessment of the insurance business, such as a portfolio valuation or a solvency investigation based on internal models. The case of life annuities is in particular addressed, due to the importance of mortality/longevity on the cost of living benefits for the elderly. Our aim is to describe a stochastic mortality model calibrated on the best-estimate life table available to the insurer and to the mortality experienced in the insurer's portfolio. As we address life annuities, uncertainty of future mortality improvements, i.e. the aggregate mortality/longevity risk, needs in particular to be accounted for. Following Olivieri and Pitacco (ASTIN Bull 39(2):541-563, 2009), we extend some classical results about the modeling of the number of deaths joint to the modeling of parameter uncertainty. We explore the features of two alternative approaches: a Beta-Binomial and a Poisson-Gamma setting; we then focus on the latter only. Thanks to a Bayesian inferential procedure, the parameters, initially assigned referring to the best-estimate life table, are updated according to the mortality experienced in the portfolio. Extending a traditional tool-kit, the framework we define is in particular suitable for practical work. Due to calibration, clearly the scope of the model is within internal assessments. To provide an example of application of the model, we perform a capital assessment. Solvency rules which could be adopted as an alternative to a standard, regulatory requirement are tested. The Solvency 2 requirement for longevity risk is referred to for the design of an internal rule which could get validation for replacing the standard one.

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Frailty-based Lee–Carter family of stochastic mortality models

Carannante,

D’Amato,

Haberman

et al. 2023

Qual Quant

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In the actuarial literature, frailty is defined to be the unobserved variable which encompasses all the factors affecting human mortality other than gender and age. Heterogeneity in individual frailty can play a significant role in population mortality dynamics. In the present paper, we identify the main latent factors that explain the frailty component, in order to clarify its role in mortality projections. We show, using longitudinal survey data, that frailty is mainly due to co-morbidities that impact on the process of deterioration in terms of the human body’s physiological capacity. Accordingly, we provide frailty-based stochastic models for projecting mortality based on the Lee–Carter family of models. We propose several versions that consider frailty both as an age-dependent and a time-dependent factor and also combining the interaction effects of age and time in comparison with the general level of mortality, and compare the resulting mortality projections using data from England.

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Heterogeneity in Survival Models - Applications to Pensions and Life Annuities

Cited by 23 publications

References 46 publications

Frailty and Risk Classification for Life Annuity Portfolios

Frailty and Risk Classification for Life Annuity Portfolios

Stochastic mortality: experience-based modeling and application issues consistent with Solvency 2

Frailty-based Lee–Carter family of stochastic mortality models

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