Reinsurance

A primary insurer's losses are described and you must determine cessions, retentions, and net retained losses under different reinsurance structures.

Proportional (quota share, surplus share): cede a fixed percentage of premium and losses. Excess of loss (per-risk, per-occurrence, aggregate): cede losses above an attachment up to a limit. Apply each structure to the loss distribution: for XL on a single risk, ceded loss = min(X - attachment, layer width) × (1 if X > attachment else 0).

Proportional: cede a fraction. XL: cede losses above attachment up to limit per risk/event.

A reinsurance layer (e.g., $1M xs $1M) is to be priced and you must apply the burning cost or exposure rating method.

Burning cost: historical losses in the layer / historical premium, trended and adjusted for any known changes; apply a target loss ratio. Exposure rating: apply ILFs (increased limits factors) or exposure curves to allocate the expected ground-up loss to the layer. Burning cost requires sufficient layer experience; exposure rating works for layers above the data.

Burning cost: trended layer losses / premium. Exposure rating: ground-up × loss share of layer.

A primary insurer is comparing different reinsurance programs and must evaluate the impact on retained losses, volatility, and required capital.

Simulate or analytically derive the distribution of net retained losses under each program. Compare expected retained loss, standard deviation, VaR, and TVaR. Compute the cost (reinsurance premium less ceded losses) and capital relief. Use return on capital to compare programs at the same risk level.

Retained loss distribution drives required capital; compare programs on net cost vs capital relief.