Abstract
This paper deals with the optimal retention level under four competitive criteria: survival probability, expected profit, variance and expected shortfall of the insurer’s risk. The aggregate claim amounts are assumed to be distributed as compound Poisson, and the individual claim amounts are distributed exponentially. We present an approach to determine the optimal retention level that maximizes the expected profit and the survival probability, whereas minimizing the variance and the expected shortfall of the insurer’s risk. In the decision making process, we concentrate on multi-attribute decision making methods: the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods with their extended versions. We also provide comprehensive analysis for the determination of the optimal retention level under both the expected value and standard deviation premium principles.
Highlights
There has been a growing interest in ruin probability, and considerable attention has been paid to determine the optimal reinsurance level under the ruin probability constraint
Since the revised VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method takes the variation between each alternative and the best value of the criterion into account, this method is insufficient in determining the optimal retention level
The results show that the optimal retention levels do not differ significantly for all methods, except the revised VIKOR method
Summary
There has been a growing interest in ruin probability, and considerable attention has been paid to determine the optimal reinsurance level under the ruin probability constraint. As a very first study, De Finetti discusses how optimal levels should be calculated for both the excess of loss and proportional reinsurance under the minimum variance criterion for the insurer’s expected profit [1]. Dickson and Waters [2] develop De Finetti’s approach and focus on minimizing the ruin probability instead of the variance criterion in [1]. Kaluszka presents the optimal reinsurance, which aims to minimize the ruin probability for the truncated stop loss reinsurance [3]. Kaishev and Dimitrova suggest a joint survival optimal reinsurance model for the excess of loss reinsurance [5]. Nie et al propose an approach to calculate the optimal reinsurance for a reinsurance arrangement in the lower barrier model with capital injection [6]. Centeno and Simoes present a survey about the state-of-the-art of optimal reinsurance [7]
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