2015/01/28 by Gildas Ratovomirija, Ratovomirija, Gildas
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #97M30 #FOS: Economics and business #FOS: Mathematics #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.1501.07297
openalex publication_date 2015/01/28 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28
In this paper, we address the aggregation of dependent stop loss reinsurance\nrisks where the dependence among the ceding insurer(s) risks is governed by the\nSarmanov distribution and each individual risk belongs to the class of Erlang\nmixtures. We investigate the effects of the ceding insurer(s) risk dependencies\non the reinsurer risk profile by deriving a closed formula for the distribution\nfunction of the aggregated stop loss reinsurance risk. Furthermore,\ndiversification effects from aggregating reinsurance risks are examined by\nderiving a closed expression for the risk capital needed for the whole\nportfolio of the reinsurer and also the allocated risk capital for each\nbusiness unit under the TVaR capital allocation principle. Moreover, given the\nrisk capital that the reinsurer holds, we express the default probability of\nthe reinsurer analytically. In case the reinsurer is in default, we determine\nanalytical expressions for the amount of the aggregate reinsured unpaid losses\nand the unpaid losses of each reinsured line of business of the ceding\ninsurer(s). These results are illustrated by numerical examples.\n