We can see that for fixed value of initial surplus u and the impact of the dependence parameters range from −1 to 1, the ruin probabilities decrease.
In addition, as indicated above, we assume the dependence parameters for MZ and DZ twins to be independent.
Using the special relationships among relative pairs, we can implement the dependence parameters in the copula via the relationships among kinship coefficients, Kendall's tau and the copula dependence parameters without estimation.
As the kinship coefficients are already known as in Table 1, we get Kendall's tau by the above relationships and in turn, the dependence parameters in the copula model is obtained from the relationship among the dependence parameters and kendal's tau for specified copula.
Genest et al. (1995) suggested a pseudo-likelihood approach to estimate the dependence parameters, in which the observed data is transformed via the empirical marginal distributions to obtain pseudo-data that are used in the estimation.
For this copula, Spearman's rho (Kendall's tau) and the dependence parameters θ ij's in normal copula are related by (Lindskog, 2000) By relationships (6) and (7), the dependence parameters θ ij's in the multivariate normal copula are easily obtained given the τ ij's, which are computed via the known kinship coefficients Δ kij's, as long as we know the kin type of relative pair (i, j).
The reason for this result is that the intensity and average rate of claims both decrease as the dependence parameter increases (see Proposition 1 and Remark 3).
The dependence parameter of the conditional copula possibly depends on the value of the covariate vector.
In simulations it is shown that the test performs well (even under misspecification of the copula family and/or the dependence parameter structure) in comparison to available tests designed for testing for constancy of the dependence parameter.
Finally, notice the estimate for the dependence parameter rho (0.3652).
