Shared Compound Frailty Model With Application in Joint Life Annuity Insurance
Abstract
Observable risk factors (e.g., health condition) can explain heterogeneity in
mortality among assureds; but modeling the risk profile of a heterogeneous
life from unobservable risk factors, such as genetics is complex. This limits
the application of only reported rating classes adopted for underwritten
annuities. Insurance firms routinely disregard unreported risk factors perhaps
because of difficulties in modeling. Although a number of research has
been done in univariate frailty modeling to account for unobserved risks, the
widely applied frailty mixture is the gamma. One major drawback of the
gamma is that it is time-invariant. The scientific interest of the study is
to account for time-varying heterogeneity using compound processes. For
single-life insurance contracts, the non-central gamma compound process is
suggested with the generalized exponential and generalized Weibull baselines
to account for time-varying frailties and carry out valuations. On the
other hand, grouping insureds in clusters such as joint annuities imposes
statistical dependence between lifetimes. The dependence is a result of an
unreported risk factor called the frailty that represents a weighted sum of
shared lifestyles on mortality risk of group members. In fact, standard insurance
valuation considers independence when pricing joint-life products.
Different approaches to dependence modeling have been proposed in literature.
However, these models consider separately either only the negative
effects of dependence alone or positive effect of dependence. The study further
proposes to apply the shared compound frailty approach in valuation of
joint annuities to address time-varying heterogeneity effects positively and
negatively associated with dependence. The positive stable distribution used
entails the frailty distribution with the weighted exponential, generalized exponential
and weighted Weibull as the base force of mortality distributions.
In this study, Bayes inference based on Gibbs sampling is used to calibrate
the base force of mortality distributions using a large Kenyan insurer term
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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