Stochastic Mortality Modelling for Dependent Coupled Lives

Abstract

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.

Pricing Marriage Insurance with Mortality Dependence

“…Finally, applying ( 19) and ( 21) to (18), we obtain (10). Moreover, ( 13) results from the property of the transition matrix.…”

Exploring Multivariate Copula Models and Fuzzy Interest Rates in Assessing Family Annuity Products

“…Multiple life annuity data from census data in the Netherlands, insurance companies in France, and genealogical data in France about married couples (Sanders & Melenberg, 2016;Lu, 2017;Cabrignac et al, 2020). Furthermore, studies on joint life annuities and last survivors from survey data in Ghana and insurance companies in Kenya (Henshaw et al, 2020;Walter et al, 2021). Based on existing research, the last two studies examined inter-annual dependency in a socioeconomic context.…”

The Benefits of Family Annuity Calculation With Vine’s Copula and Fuzzy Interest Rate

“…The use of the Archimedean Copula family is more widely used than the Eliptical Copula family which is less able to capture asymmetric data shapes in joint life span modeling [5]. Furthermore, studies on joint life annuities from survey data in Ghana [6]. The dependency pattern of more than 2 random variables using one Copula cannot capture the dependency between random variables specifically.…”