Approximations for life annuity contracts in a stochastic financial environment

Hoedemakers, Tom; Darkiewicz, Grzegorz; Goovaerts, Marc

doi:10.1016/j.insmatheco.2005.02.003

Cited by 16 publications

(11 citation statements)

References 28 publications

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“…This is not surprising. From Example 1 in Hoedemakers, Darkiewicz, and Goovaerts (2005) it immediately follows that and hence for any d > 0 one has …”

Section: Numerical Illustrationsmentioning

confidence: 99%

Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables

Darkiewicz¹,

Deelstra²,

Dhaene³

et al. 2009

J of Risk & Insurance

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We investigate lower and upper bounds for right tails (stop-loss premiums) of deterministic and stochastic sums of nonindependent random variables. The bounds are derived using the concepts of comonotonicity, convex order, and conditioning. The performance of the presented approximations is investigated numerically for individual life annuity contracts as well as for life annuity portfolios, where mortality is modeled by Makeham's law, whereas investment returns are modeled by a Brownian motion process. Copyright (c) The Journal of Risk and Insurance, 2009.

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“…This is not surprising. From Example 1 in Hoedemakers, Darkiewicz, and Goovaerts (2005) it immediately follows that and hence for any d > 0 one has …”

Section: Numerical Illustrationsmentioning

confidence: 99%

Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables

Darkiewicz¹,

Deelstra²,

Dhaene³

et al. 2009

J of Risk & Insurance

Self Cite

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“…In this paper, we wish to remedy this situation by extending the results of Dhaene et al (2002ab, 2004, Hoedemakers et al (2005) and Vanduffel et al (2005) 1 where the authors develop bounds in a sense of convex order to yield an approximating sequence for sums of log-normal dependent random variables. In contrast to the work done by Dhaene et al (2002a,b) where authors and approximations for a single signed stream of cash flows we extend their idea of comonotonic approximations to the case of positive and negative cash flows (i.e.…”

Section: Introductionmentioning

confidence: 98%

Comonotonic approximations for a general pension problem

Ahčan

2011

IJSE

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In this paper, we search for such an investment strategy that minimises the probability of default (or lifetime ruin probability) given a fixed investment amount during the accumulation phase and a fixed withdrawal rate during the annuitisation part. In solving the above-mentioned problem, we introduce a methodology that helps us to obtain a solution in analytical fashion without resorting to time consuming Monte Carlo (MC) simulation. More precisely, the existing methodology of conditioning Taylor approximation is used to find a solution by approximating the original sum via a comonotonic sum. More specifically, we searched for the optimal multi-period investment strategy of an investor whose accumulation phase (lasting M years) is followed by an annuitisation period (lasting N years). When choosing the optimal asset mix, we restricted our analysis to the class of constant mix dynamically rebalanced strategies, with optimisation criterion set to the probability of default. As it was shown by means of a numerical illustration, the solutions of our approximate procedure closely relate to the results of MC simulation.

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“…interest rates, while Parker (1994) presented an approximation to the limiting distribution of the present value of the benefits of a portfolio of temporary insurance contracts. Using the concept of comonotonicity, Hoedemakers et al (2005) proposed an Nolde and Parker (2014) derived a recursive formula for calculating the distribution function of the accounting surplus for a portfolio of homogeneous life policies, where the accounting surplus at a future valuation time is defined as the difference between the value of assets and the actuarial reserve at that time. The paper also illustrated the approximation of the distribution of the surplus per policy for a limiting portfolio (i.e., when the size of the portfolio goes to infinity).…”

Section: Introductionmentioning

confidence: 99%