The joint mortality of couples in continuous time

Stochastic Mortality Modelling for Dependent Coupled Lives

“…Considering for the first time to the best of our knowledge the existence of socioeconomic influences on dependence between coupled lives and the bereavement process of surviving spouses in less economically developed populations, we utilise analysis of a Ghanaian dataset within which a lesser initial concentration of broken-heart syndome is observed to inform the proposal of a joint mortality model. In line with our observations which fit the nature of a reduced volatility and following the results of , we introduce correlated non-mean-reverting Cox-Ingersoll-Ross diffusions as paired mortality intensities, defining a model of the joint mortality of a couple assumed to share the same socioeconomic environment based on the stochastic mortality model proposed by Jevtić and Hurd (2017). A mean-reverting Ornstein-Uhlenbeck process is selected to represent the influence the loss of a spouse has on the remaining lifetime of the surviving partner.…”

“…Although dependence due to unobserved risk factors is not considered by Dufresne et al (2018), incorporation of age difference and sex of the elder spouse in definition of the level of association between coupled lifetimes in a copula model, supports suggestion of asymmetric dependence. Jevtić and Hurd (2017) introduce an alternative to copula dependence in the credit risk environment through definition of a probabilistic mechanism describing the influence the primary death has on the bereaved spouse. A stochastic mortality model of affine type is implemented for mortality experience, assuming correlated non-mean-reverting Ornstein-Uhlenbeck diffusions for the mortality intensities of coupled lives.…”

“…Inclusion of the probabilistic framework in the stochastic mortality model proposed by Jevtić and Hurd (2017) prompted the decision to implement a similar model within our investigation. Whilst multiple state models such as the semi-Markov chain model applied by Ji et al (2011) offer transparency and the ability to observe whether the level of risk changes following a death event, the probabilistic mechanism also enables incorporation of the health of both members of a couple prior to the primary death.…”

“…Although we focus on the short-term dependence of coupled lives, the model proposed is capable of addressing both short-and long-term structures, with the ability to encompass any existence of dependence between two lifetimes before the death of one spouse. In this section, we propose an adaptation of the stochastic mortality model with probabilistic framework described by Jevtić and Hurd (2017), first defining a number of important concepts for survival analysis.…”

Some Results on Measures of Interaction between Paired Risks

“…It has been confirmed that there exists dependence between lifetimes of a couple. For more discussions on the dependence of couple's mortalities, one may refer to (Denuit et al 2001;Jagger and Sutton 1991;Jevtić and Hurd 2017). When measuring the contribution of a component to systemic risk, usually the risk of this institution and the risk of another institution or even the whole system will be jointly considered as paired risks.…”