Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of...

Insurance and reinsurance live and die from the diversification benefits or lack of it in their risk portfolio. The new solvency regulations allow companies to include diversification in their computation of risk-based capital (RBC). The question is how to really evaluate those benefits.To...

In this paper we compare the diversification benefit of portfolios containing excess-of-loss treaties and portfolios containing quota-share treaties, when the risk measure is the (excess) Value-at-Risk or the (excess) Expected Shortfall. In a first section we introduce the set-up under which we...

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its...

With a simple example of throwing a die, we show how to price an insurance policy. We further study how this price decreases when many similar policies are sold. The diversification benefits increase with the number of policies and similarly the risk loading of the premium required for the risk...