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.
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