TY - JOUR
T1 - Effect of stop-loss reinsurance on the primary insurer solvency
AU - Constantinescu, Corina
AU - Dias, Alexandra
AU - Li, Bo
AU - Siska, David
AU - Wang, Simon
PY - 2022/10/10
Y1 - 2022/10/10
N2 - Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the economic capital, or the required initial capital to hold, corresponding to the 99.5% value-at-risk of its surplus. Specifically, we show that under a stop-loss contract, the ruin probability for the primary insurer, for both a finite- and infinite-time horizon, can be obtained from the finite-time ruin probability when no reinsurance is bought. We develop a finite-difference method for solving the (partial integro-differential) equation satisfied by the finite-time ruin probability with no reinsurance, leading to numerical approximations of the ruin probabilities under a stop-loss reinsurance contract. Using the method developed here, we discuss the interplay between ruin probability, reinsurance retention level and initial capital.
AB - Stop-loss reinsurance is a risk management tool that allows an insurance company to transfer part of their risk to a reinsurance company. Ruin probabilities allow us to measure the effect of stop-loss reinsurance on the solvency of the primary insurer. They further permit the calculation of the economic capital, or the required initial capital to hold, corresponding to the 99.5% value-at-risk of its surplus. Specifically, we show that under a stop-loss contract, the ruin probability for the primary insurer, for both a finite- and infinite-time horizon, can be obtained from the finite-time ruin probability when no reinsurance is bought. We develop a finite-difference method for solving the (partial integro-differential) equation satisfied by the finite-time ruin probability with no reinsurance, leading to numerical approximations of the ruin probabilities under a stop-loss reinsurance contract. Using the method developed here, we discuss the interplay between ruin probability, reinsurance retention level and initial capital.
KW - Finite-difference method
KW - Reinsurance
KW - Ruin probability
KW - Stop-loss
UR - http://www.scopus.com/inward/record.url?scp=85140456579&partnerID=8YFLogxK
U2 - 10.3390/risks10100193
DO - 10.3390/risks10100193
M3 - Article
AN - SCOPUS:85140456579
SN - 2227-9091
VL - 10
JO - Risks
JF - Risks
IS - 10
M1 - 193
ER -