Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

Abstract EN

This paper aims to provide a practical optimal reinsurance scheme underparticular conditions, with the goal of minimizing total insurer risk.

Excessof loss reinsurance is an essential part of the reinsurance market, but the conceptof stop-loss reinsurance tends to be unpopular.

We study the purchasearrangement of optimal reinsurance, under which the liability of reinsurers islimited by the excess of loss ratio, in order to generate a reinsurance schemethat is closer to reality.

We explore the optimization of limited stop-lossreinsurance under three risk measures: value at risk (VaR), tail value at risk(TVaR), and conditional tail expectation (CTE).

We analyze the topic fromthe following aspects: (1) finding the optimal franchise point with limitedstop-loss coverage, (2) finding the optimal limited stop-loss coverage withina certain franchise point, and (3) finding the optimal franchise point withlimited stop-loss coverage.

We provide several numerical examples.

Our resultsshow the existence of optimal values and locations under the variousconstraint conditions.