Information Entropy Method In Reinsurance

When an insurance company does a reinsurance decision-making, it needs to choose an optimal reinsurance. choosing an optimal reinsurance mainly contains two aspects: one is to choose the formation of reinsurance, the other is to make out the parameters for the reinsurance. Based on the information entropy theory, this dissertation gives a research on the problems, and proposes corresponding models and computational algorithms. There are five chapters in the dissertation as following:Chapter 1 is introduction. In this chapter, backgrounds and meaning of the theme selection, the history of the reinsurance theory, reinsurance models and its research methods are introduced.Chapter 2 is preliminaries. In this chapter, the relative conceptions, basic mathematical models for reinsurance and the basic principles in pricing premium and the characteristics of premium function are introduced.Chapter 3. Simple comparability between the entropy and the variance is introduced firstly. From the angle of dispersion orderings, the equivalence of entropy and variance is discussed, then after the entropies and variances of several important discrete and continuous distributions being listed, we find that they have coherent monotonies.Chapter 4. After the analysis of the limitations of measuring risk with variance on the base of Markowitz mean-variance in confirming the optimal proportion, a measure method for the risk based on the concept of entropy is developed and that can be used as an efficient complementarity for measuring risk with variance. On this basis, a new model: mean-variance-entropy model, using entropy and variance together to measure risk, is proposed, and the example shows the practicability of the model.Chapter 5. Discussions on the optimization of stop-loss reinsurance are given firstly, and then utilizing the minimum cross-entropy principle, optimization model is established, and the upper and lower bounds of the stop-loss premium are given.The conclusion of the paper is that the information entropy theory can be used as a good tool on the reinsurance research.