Mortality Credits Within Large Survivor Funds

Denuit, Michel; Hieber, Peter; Robert, Christian

doi:10.1017/asb.2022.13

Cited by 12 publications

(4 citation statements)

References 23 publications

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“…. , m. Sharing rules which satisfy Property 3.1 are discussed in Sabin (2010Sabin ( , 2011, and sharing rules for the case where payments are made to just deceased members are described in, for example, Bernhardt and Donnelly (2018), Lucas (2022), andDenuit et al (2022), and the references therein.…”

Section: Intuitionmentioning

confidence: 99%

“…Several previous studies have specified payments to the estates of members who die in (see, e.g., Bernhardt and Donnelly, 2018; Hieber and Lucas, 2022; Denuit et al. , 2022).…”

Section: Overview Of Individual Tontine Accountsmentioning

confidence: 99%

“…This will maximize tontine gains of survivors, which is the focus of the current study. Several previous studies have specified payments to the estates of members who die in (t i−1 , t i ) (see, e.g., Bernhardt and Donnelly, 2018;Hieber and Lucas, 2022;Denuit et al, 2022).…”

Section: Intuitionmentioning

confidence: 99%

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Optimal performance of a tontine overlay subject to withdrawal constraints

Forsyth,

Vetzal,

Westmacott

2023

ASTIN Bull.

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We consider the holder of an individual tontine retirement account, with maximum and minimum withdrawal amounts (per year) specified. The tontine account holder initiates the account at age 65 and earns mortality credits while alive, but forfeits all wealth in the account upon death. The holder wants to maximize total withdrawals and minimize expected shortfall at the end of the retirement horizon of 30 years (i.e., it is assumed that the holder survives to age 95). The holder controls the amount withdrawn each year and the fraction of the retirement portfolio invested in stocks and bonds. The optimal controls are determined based on a parametric model fitted to almost a century of market data. The optimal control algorithm is based on dynamic programming and the solution of a partial integro differential equation (PIDE) using Fourier methods. The optimal strategy (based on the parametric model) is tested out of sample using stationary block bootstrap resampling of the historical data. In terms of an expected total withdrawal, expected shortfall (EW-ES) efficient frontier, the tontine overlay dramatically outperforms an optimal strategy (without the tontine overlay), which in turn outperforms a constant weight strategy with withdrawals based on the ubiquitous four per cent rule.

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Section: Intuitionmentioning

confidence: 99%

“…Several previous studies have specified payments to the estates of members who die in (see, e.g., Bernhardt and Donnelly, 2018; Hieber and Lucas, 2022; Denuit et al. , 2022).…”

Section: Overview Of Individual Tontine Accountsmentioning

confidence: 99%

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Optimal performance of a tontine overlay subject to withdrawal constraints

Forsyth,

Vetzal,

Westmacott

2023

ASTIN Bull.

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“…Fortunately, the OGF method provides a numerical solution to compute the expected allocations without further notions of number theory. See also Example 4.1 of [Denuit et al, 2021] for a situation where no diversification occurs for some participants due to partitions of odd numbers.…”

Section: Application: Small Portfolio Of Heterogeneous Claimsmentioning

confidence: 99%

Generating function method for the efficient computation of expected allocations

Blier-Wong¹,

Cossette²,

Marceau³

2022

Preprint

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Consider a risk portfolio with aggregate loss random variable S = X 1 + • • • + X n defined as the sum of the n individual losses X 1 , . . . , X n . The expected allocation, E[X i × 1 {S=k} ], for i = 1, . . . , n and k ∈ N, is a vital quantity for risk allocation and risk-sharing. For example, one uses this value to compute peer-to-peer contributions under the conditional mean risk-sharing rule and capital allocated to a line of business under the Euler risk allocation paradigm. This paper introduces an ordinary generating function for expected allocations, a power series representation of the expected allocation of an individual risk given the total risks in the portfolio when all risks are discrete. First, we provide a simple relationship between the ordinary generating function for expected allocations and the probability generating function. Then, leveraging properties of ordinary generating functions, we reveal new theoretical results on closed-formed solutions to risk allocation problems, especially when dealing with Katz or compound Katz distributions. Then, we present an efficient algorithm to recover the expected allocations using the fast Fourier transform, providing a new practical tool to compute expected allocations quickly. The latter approach is exceptionally efficient for a portfolio of independent risks.

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Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools

Denuit,

Robert

2024

Methodol Comput Appl Probab

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Mortality Credits Within Large Survivor Funds

Cited by 12 publications

References 23 publications

Optimal performance of a tontine overlay subject to withdrawal constraints

Optimal performance of a tontine overlay subject to withdrawal constraints

Generating function method for the efficient computation of expected allocations

Conditional Mean Risk Sharing of Independent Discrete Losses in Large Pools

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