Heavy-tailed insurance portfolios: buffer capital and ruin probabilities

We study the risk of insolvency for an insurance company with mul-tiple business lines facing large claims with heavy-tailed distribution. The company is allowed to transfer capital between business lines but such capital transfers are restricted by regulations. The same princi-ples apply to an insurance group with agreements of mutual financial support in case of large losses. The insurance company is considered insolvent when negative positions in one or several lines of business cannot be canceled by means of capital transfer. Under the assump-tion that the distribution of the vector of claim sizes is multivariate regularly varying we derive the asymptotic decay of the ruin probabil-ity as the initial capital tends to infinity. In particular, we analyze the impact of rules for transfer of capital on the ruin probability and we draw conclusions about possible benefits from diversification. We also analyze the asymptotic behavior of the buffer capital, defined as the smallest amount of capital needed to reduce the ruin probability to a prespecified level, as the level tends to zero. A Poisson shock model serves as a useful example for which explicit computations are possible and diversification effects can be quantified. Key words: Ruin probabilities; buffer capital; regular variation; re-newal model; diversification 1