THE DETERMINATION OF AN OPTIMAL RETENTION OF A STOP-LOSS REINSURANCE BASED ON AN EARTHQUAKE CATASTROPHE MODEL - Ferer Christian W., Vincensius
Indonesia is located at the meeting point of the world’s four major plates; hence it is prone to tectonic earthquakes which may cause very large financial losses. To manage this risk, reinsurance is used as an effort for risk sharing, particularly for large losses. In a stop-loss reinsurance contract, a higher retention level increases the risk retained by an insurance company (insurer or cedent), but reduces the reinsurance premium due to a decrease in the loss transferred to a reinsurance company (reinsurer); and vice versa. This thesis addresses the trade-off problem by determining an optimal retention level that minimizes the value-at-risk (VaR) and the tail value-at-risk (TVaR) risk measures of the cedent's total cost with a reinsurance risk premium calculated using the expected, variance, and standard deviation premium principles. In addition, optimal retentions in multilayer stoploss reinsurance where the reinsurer reinsures its company to another reinsurance company(s) are also discussed. In this thesis, the determination of an optimal retention based on the distribution of the aggregate loss data that follows a lognormal distribution, obtained from an event loss table (ELT) of an Earthquake Catastrophe (CAT) Model, is discussed. The ELTs are constructed based on the distribution of the moment magnitudes of the historical tectonic earthquake mainshocks data. The moment magnitudes are modelled by a generalized Pareto distribution based on a given average recurrence interval. These methodologies are applied to financial loss data due to tectonic earthquakes on residential buildings in the Papua Region, Indonesia. The optimal retention obtained is then applied in an earthquake disaster risk financing strategy in accordance with the financing scheme set by the Fiscal Policy Agency, Ministry of Finance of the Republic of Indonesia.