Optimal Reinsurance Under Standard Deviation Calculation Principle And Mean Square Error Risk Measure

This paper concerns the problem of how to purchase reinsurance in order to make the insurer and reinsurer's total risk least under standard deviation calculation principle.It is assumed that the reinsurer's risk and the insurer's deviation must be less than proper constants respectively. Here,for the risk of the reinsurer,we adopt variance risk measure;for the risk of the insurer,we adopt mean square error risk measure,and also we find out sufficient conditions for the optimality of reinsurance arrangement,at last,the process of solution is illustrated by an example.There are four parts in this paper:1.An introduction to reinsurance,including the kinds of reinsurance strategy and premium calculation principles.2.In this chapter we introduce Convex function,G(?)teaux derivative and so on,which are useful for the proof of lemmas and theorems.3.This chapter is the core of this paper,we obtain optimal reinsurance under standard deviation calculation principle.By the method of Lagrange,sufficient conditions for the optimality of reinsurance contract are given under standard deviation calculation principle.In this chapter,we adopt variance risk measure and mean square error risk measure respectively for the risk of the reinsurer and the risk of the insurer,and we find out sufficient conditions for the optimality of reinsurance arrangement,at last,we provide an example to explain the result.4.In this chapter we obtain the optimal reinsurance arrangement under expectation calculation.In this paper,there are proofs and illustrations for theories,maybe it can make sense to reinsurance in practice to some extent.