Effect of Stop-Loss Reinsurance on Primary Insurer Solvency

Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their company. Ruin probabilities allow us measure the effect stop-loss on solvency primary insurer. They further permit calculation economic capital, or required initial capital hold, corresponding 99.5% value-at-risk its surplus. Specifically, we show under contract, ruin probability for insurer, both finite- and infinite-time horizon, can be obtained from finite-time when no bought. We develop finite-difference method solving (partial integro-differential) equation satisfied by with reinsurance, leading numerical approximations contract. Using developed here, discuss interplay between probability, retention level capital.