Optimal Reinsurance Strategy

Reinsurance is on the basis of the insurance contract, by singing sub-contract, and transfer risk to other insurance companies. In according to reinsurance premiums and total premiums weather equal to the ratio of mean reinsurer's share of compensation and total compensation. we divide it into the ratio of proportional reinsurance and non-proportional reinsurance. In which the proportion of proportional reinsurance, including quote-share reinsurance, excess of loss reinsurance, the mixture of Quota share and excess of loss reinsurance. non-proportional reinsurance, including excess of loss reinsurance, stop loss reinsurance and the largest claims reinsurance.This paper mainly studies the classical risk model and the Sparre Anderson risk model, the classical risk model is using conditional extreme value optimization method, solves for the adjustment coefficient of maximum, And prove the adjustment coefficient is about the limit of the specified amount oneself single-peak function and what is the circumstances have retained amount, using the theory explains adjustment coefficient when the maximum probability. The mainly conclusion is:Theorem 3.2.2 Considering the classical risk model of index distribution model and reinsurance f^B form.let a≥a₀,haveWe get (1) the insure of the adjustment coefficient R_a,M is about M of the showing function.(2) R_a,M gets the maximum value at R'=M^-1ln[(1+α)γ].On the basis of the Sparre Anderson risk model ,the research makes the reinsurance model suit for the reality. In this model the adjustment coefficient is as the reinsurance and excess loss reinsurance mixed model of the underwriter taking the specified amount oneself. the premium the calculation principle of the premium si according to expectations. Proof of reinsurance person get extreme value at certain point. The mainly conclusion is:Theorem 4.2.1 For a fixed value a∈(a₀,1], R_a,M is a Single function about M ,Can get the maximum value meet R_a,M is the only solution about g_a,M(r)=1. Theorem 4.2.1 For a fixed value a∈(a₀,1],let R_a is the maximum value about R_a,M, R_a is the maximum value about R_a,M,at a=1can get the maximum value, if and only if...