The conditional Haezendonck–Goovaerts risk measure

Abstract The Haezendonck–Goovaerts (HG) risk measure has received increasing attention in recent years. In this paper, we propose a conditional version of the HG risk measure, called CoHG risk measure. This conditional risk measure can be used to describe a causality relationship between two risk variables and to qualify the systemic risk contribution of a risk in a catastrophic scenario. We list some basic properties of the CoHG risk measure and show for it an analytical expression, which however involves the solution to an implicit equation. This expression can be made completely explicit for a power or exponential Young function. Finally, we conduct a numerical study to show the trend of the CoHG risk measure in certain risk parameters.