Abstract
Reinsurance is available for a reinsurance premium that is determined
according to a convex premium principle H. The first insurer selects the
reinsurance coverage that maximizes its expected utility. No conditions are
imposed on the reinsurer’s payment. The optimality condition involves the
gradient of H. For several combinations of H and the first insurer’s utility
function, closed-form formulas for the optimal reinsurance are given. If H is
a zero utility principle (for example, an exponential principle or an expectile
principle), it is shown, by means of Borch’s Theorem, that the optimal
reinsurer’s payment is a function of the total claim amount and that this
function satisfies the so-called 1-Lipschitz condition. Frequently, authors
impose these two conclusions as hypotheses at the outset.
according to a convex premium principle H. The first insurer selects the
reinsurance coverage that maximizes its expected utility. No conditions are
imposed on the reinsurer’s payment. The optimality condition involves the
gradient of H. For several combinations of H and the first insurer’s utility
function, closed-form formulas for the optimal reinsurance are given. If H is
a zero utility principle (for example, an exponential principle or an expectile
principle), it is shown, by means of Borch’s Theorem, that the optimal
reinsurer’s payment is a function of the total claim amount and that this
function satisfies the so-called 1-Lipschitz condition. Frequently, authors
impose these two conclusions as hypotheses at the outset.
| Original language | English |
|---|---|
| Pages (from-to) | 62-79 |
| Number of pages | 18 |
| Journal | Scandinavian Actuarial Journal |
| Volume | 2019 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 15 Jan 2019 |
| Externally published | Yes |