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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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