The Effect of the Retention Limit on the Risk Reserve

Abstract

This paper is devoted to the study of the initial reserve, as a function of the retention limit, needed to assure that the probability of ruin, at the end of a certain period of time, is not higher than an agreed value, for an excess of loss treaty. To assess the probability of ruin, the normal and the normal power approximation are used. It is shown that the initial reserve is not in general an increasing function of the retention, having a minimum under fair assumptions. KEYWORDSRisk reserve; excess of loss; normal power approximation; normal approximation.

Retention and Reinsurance Programmes

“…Still using the normal power approximation and under some fair assumptions (see [18]), it was shown that it has a minimum, which rends feasible the formulation of the problem as the determination of the retention limit to minimize the initial reserve that will give a one year ruin probability of at most . However, this function is not always increasing.…”

“…where α is the loading coefficient on the excess-ofloss reinsurance premium (assumed to be calculated See [18] for the conditions obtained when the normal power is used instead of the normal approximation. Note that although the use of the normal approximation is questionable, because when M increases the distribution of Y becomes skewer and skewer, the optimal value given by (5) does not differ much from the corresponding value obtained when the approximation used is the normal power.…”

The Effect of Non-Proportional Reinsurance: A Revision of Solvency II Standard Formula

“…We also evaluate the effect of a different retention limit (see Figure 6). The attachment point has been evaluated as L LoB = E(Z gross pre,LoB ) + S · σ(Z gross pre,LoB ), where alternative values of S have been tested (see also De Lourdes Centeno (1995) for an analysis of the effect of retention limit on risk reserve). As expected, a greater retention limit leads to a reduction in NP LoB .…”