Before revision:  Such a construction is more parsimonious and tractable in higher dimensions than plain vanilla common shock models. We also consider practical implementation and explicitly incorporate known covariates , such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes( or at least help tease out those relationships ).
After revision:  In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events. The explicit incorporation of time-varying, known covariates can accommodate characteristics of real data and hence facilitate implementation in practice. In an insurance context, these could be changes in policy volumes over time, as well as seasonality patterns and trends, which may explain some of the relationship between two insurance processes( or at least help tease out those relationships ).