Multivariate higher order moments in multi-state life insurance

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Multivariate higher order moments in multi-state life insurance. / Ahmad, Jamaal.

In: Scandinavian Actuarial Journal, Vol. 2022, No. 5, 2022, p. 399-420.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Ahmad, J 2022, 'Multivariate higher order moments in multi-state life insurance', Scandinavian Actuarial Journal, vol. 2022, no. 5, pp. 399-420. https://doi.org/10.1080/03461238.2021.1989025

APA

Ahmad, J. (2022). Multivariate higher order moments in multi-state life insurance. Scandinavian Actuarial Journal, 2022(5), 399-420. https://doi.org/10.1080/03461238.2021.1989025

Vancouver

Ahmad J. Multivariate higher order moments in multi-state life insurance. Scandinavian Actuarial Journal. 2022;2022(5):399-420. https://doi.org/10.1080/03461238.2021.1989025

Author

Ahmad, Jamaal. / Multivariate higher order moments in multi-state life insurance. In: Scandinavian Actuarial Journal. 2022 ; Vol. 2022, No. 5. pp. 399-420.

Bibtex

@article{bc22bd3bb2a04a888cb8fef9883da1e5,
title = "Multivariate higher order moments in multi-state life insurance",
abstract = "It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the unsystematic mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. Numerical examples are shown in a disability model and a spouse model to illustrate applicability of the results on insurance of a single life as well as two dependent lives.",
author = "Jamaal Ahmad",
year = "2022",
doi = "10.1080/03461238.2021.1989025",
language = "English",
volume = "2022",
pages = "399--420",
journal = "Scandinavian Actuarial Journal",
issn = "0346-1238",
publisher = "Taylor & Francis Scandinavia",
number = "5",

}

RIS

TY - JOUR

T1 - Multivariate higher order moments in multi-state life insurance

AU - Ahmad, Jamaal

PY - 2022

Y1 - 2022

N2 - It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the unsystematic mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. Numerical examples are shown in a disability model and a spouse model to illustrate applicability of the results on insurance of a single life as well as two dependent lives.

AB - It is well-known that combining life annuities and death benefits introduce opposite effects in payments with respect to the unsystematic mortality risk on the lifetime of the insured. In a general multi-state framework with multiple product types, such joint effects are less trivial. In this paper, we consider a multivariate payment process in multi-state life insurance, where the components are defined in terms of the same Markovian state process. The multivariate present value of future payments is introduced, and we derive differential equations and product integral representations of its conditional moments and moment generating function. Special attention is given to pair-wise covariances between two present values, where results closely connected to Hattendorff type of results for the variance are derived. Numerical examples are shown in a disability model and a spouse model to illustrate applicability of the results on insurance of a single life as well as two dependent lives.

U2 - 10.1080/03461238.2021.1989025

DO - 10.1080/03461238.2021.1989025

M3 - Journal article

VL - 2022

SP - 399

EP - 420

JO - Scandinavian Actuarial Journal

JF - Scandinavian Actuarial Journal

SN - 0346-1238

IS - 5

ER -

ID: 280899827