2017/10/30 by Zied Ben Salah, Salah, Zied Ben, José A. Garrido +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #60G51 (Primary) 62P05 (Secondary) #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Economics and business #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.1710.11065
openalex publication_date 2017/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a risk model where deficits after ruin are covered by a new type\nof reinsurance contract that provides capital injections. To allow the\ninsurance company's survival after ruin, the reinsurer injects capital only at\nruin times caused by jumps larger than a chosen retention level. Otherwise\ncapital must be raised from the shareholders for small deficits. The problem\nhere is to determine adequate reinsurance premiums. It seems fair to base the\nnet reinsurance premium on the discounted expected value of any future capital\ninjections. Inspired by the results of Huzak et al. (2004) and Ben Salah (2014)\non successive ruin events, we show that an explicit formula for these\nreinsurance premiums exists in a setting where aggregate claims are modeled by\na subordinator and a Brownian perturbation. Here ruin events are due either to\nBrownian oscillations or jumps and reinsurance capital injections only apply in\nthe latter case. The results are illustrated explicitly for two specific risk\nmodels and in some numerical examples.\n