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Article

Stochastic Mortality Modelling for Dependent Coupled Lives

1
Institute for Financial and Actuarial Mathematics, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK
2
African Institute for Mathematical Sciences Ghana, Legon, P. O. Box LGDTD 20046 Accra, Ghana
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2020, 8(1), 17; https://doi.org/10.3390/risks8010017
Received: 3 December 2019 / Revised: 31 January 2020 / Accepted: 5 February 2020 / Published: 11 February 2020
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics)
Broken-heart syndrome is the most common form of short-term dependence, inducing a temporary increase in an individual’s force of mortality upon the occurrence of extreme events, such as the loss of a spouse. Socioeconomic influences on bereavement processes allow for suggestion of variability in the significance of short-term dependence between couples in countries of differing levels of economic development. Motivated by analysis of a Ghanaian data set, we propose a stochastic mortality model of the joint mortality of paired lives and the causal relation between their death times, in a less economically developed country than those considered in existing studies. The paired mortality intensities are assumed to be non-mean-reverting Cox–Ingersoll–Ross processes, reflecting the reduced concentration of the initial loss impact apparent in the data set. The effect of the death on the mortality intensity of the surviving spouse is given by a mean-reverting Ornstein–Uhlenbeck process which captures the subsiding nature of the mortality increase characteristic of broken-heart syndrome. Inclusion of a population wide volatility parameter in the Ornstein–Uhlenbeck bereavement process gives rise to a significant non-diversifiable risk, heightening the importance of the dependence assumption in this case. Applying the model proposed to an insurance pricing problem, we obtain the appropriate premium under consideration of dependence between coupled lives through application of the indifference pricing principle. View Full-Text
Keywords: joint mortality; stochastic mortality; broken-heart syndrome; non-mean-reverting Cox–Ingersoll–Ross process; Ornstein–Uhleneck process; bereavement effect; socioeconomic effect; developing societies joint mortality; stochastic mortality; broken-heart syndrome; non-mean-reverting Cox–Ingersoll–Ross process; Ornstein–Uhleneck process; bereavement effect; socioeconomic effect; developing societies
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MDPI and ACS Style

Henshaw, K.; Constantinescu, C.; Menoukeu Pamen, O. Stochastic Mortality Modelling for Dependent Coupled Lives. Risks 2020, 8, 17. https://doi.org/10.3390/risks8010017

AMA Style

Henshaw K, Constantinescu C, Menoukeu Pamen O. Stochastic Mortality Modelling for Dependent Coupled Lives. Risks. 2020; 8(1):17. https://doi.org/10.3390/risks8010017

Chicago/Turabian Style

Henshaw, Kira, Corina Constantinescu, and Olivier Menoukeu Pamen. 2020. "Stochastic Mortality Modelling for Dependent Coupled Lives" Risks 8, no. 1: 17. https://doi.org/10.3390/risks8010017

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