A dynamic bivariate common shock model with cumulative effect and its actuarial application

Hyunju Lee, Ji Hwan Cha

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Standard actuarial theory of multiple life insurance traditionally postulates independence for the remaining lifetimes mainly due to computational convenience rather than realism. In this paper, we propose a general common shock model for modelling dependent coupled lives and apply it to a life insurance model. In the proposed shock model, we consider not only simultaneous deaths of the coupled members due to a single shock (e.g. a critical accident), but also cumulative effect in the mortality rate when they survive shocks. Under the model, we derive a bivariate lifetime distribution and its marginal distributions in closed forms. We study the bivariate ageing property, dependence structure and the dependence orderings of the lifetime distribution. Based on it, we investigate the influence of dependence on the pricings of insurance policies involving multiple lives which are subject to common shocks. Furthermore, we discuss relevant useful stochastic bounds.

Original languageEnglish
Pages (from-to)890-906
Number of pages17
JournalScandinavian Actuarial Journal
Issue number10
StatePublished - 26 Nov 2018


  • Common shock model
  • joint life
  • life annuities
  • shot noise process
  • stochastic dependence


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