Abstract:

We computed the HaezendonckGoovaerts risk measure of the sum of random variables with Pareto and exponential marginal distributions on different Young functions, using the inverse function of the distribution function and the properties of upper comonotonic random vector. The upper comonotonic thresholds of the portfolio risks were given. We established a transparent expression for the stoploss premium and HaezendonckGoovaerts risk measure of the total claim. We also analyzed the properties of the natural estimators of HaezendonckGoovaerts risk measures by means of numerical simulations with the help of R.

Key words:  upper comonotonicity, stoploss premium, Haezendonck-Goovaerts risk measure, tail convex order, Pareto distribution