  We propose a stochastic model allowing property and casualty insurers with
multiple business lines to measure their liabilities for incurred claims risk
and calculate associated capital requirements. Our model includes many
desirable features which enable reproducing empirical properties of loss ratio
dynamics. For instance, our model integrates a double generalized linear model
relying on accident semester and development lag effects to represent both the
mean and dispersion of loss ratio distributions, an autocorrelation structure
between loss ratios of the various development lags, and a hierarchical copula
model driving the dependence across the various business lines. The model
allows for a joint simulation of loss triangles and the quantification of the
overall portfolio risk through risk measures. Consequently, a diversification
benefit associated to the economic capital requirements can be measured, in
accordance with IFRS 17 standards which allow for the recognition of such
benefit. The allocation of capital across business lines based on the Euler
allocation principle is then illustrated. The implementation of our model is
performed by estimating its parameters based on a car insurance data obtained
from the General Insurance Statistical Agency (GISA), and by conducting
numerical simulations whose results are then presented.
