## Modelling mortality dependence with regime-switching copulas.(English)Zbl 1458.91187

The author proposes a two-regime Markov switching copula to depict the evolution of mortality dependence. One regime represents periods of high dependence and the other regime represents periods of low dependence. Each regime features a regular vine (R-vine) copula built on bivariate copulas.
A regular vine $$V$$ on $$n$$ variables is a sequence of $$n-1$$ connected trees $$T_1,T_2,\ldots,T_{n-1}$$ and satisfies the following properties:
1. $$T_1$$ is a tree with node set $$N_1=\{1,2,\ldots,n\}$$ and edge set $$E_1.$$
2. $$T_i$$ is a connected tree with node set $$N_i=E_{i-1},$$ of which the cardinality is $$n- (i-1),$$ and edge set $$E_i.$$
3. If two nodes in $$T_i,$$ for $$i=2,\ldots,n-1,$$ are joined by an edge, their corresponding edges in $$T_{i-1}$$ must share a common node.
A case study is presented to illustrate how the regime-switching copula can be applied to assess the effectiveness of longevity risk hedge with different beliefs about future mortality dependence evolution incorporated.

### MSC:

 91G05 Actuarial mathematics 91D20 Mathematical geography and demography 62P05 Applications of statistics to actuarial sciences and financial mathematics 62H05 Characterization and structure theory for multivariate probability distributions; copulas
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