20.8 Final Remarks

It should be noted that all presented models, including risk participation of reinsurers and shareholders, lead only to a modification of the distribution of the increment of the risk process. Still the mutual independence of subsequent increments and their identical distribution is preserved. There are also models where decisions concerning premiums, reinsurance, and dividends depend on current size of the capital. In general, models of this type need the stochastic control technique to be applied. Nevertheless, models presented in this chapter preserve simplicity, and allow just to have insight on long-run consequences of some decision rules, provided they remain unchanged for a long time. This insight is worthwhile despite the fact that in reality decisions are undertaken on the basis of the current situation, and no fixed strategy remains unchanged under changing conditions of the environment. On the other hand, it is always a good idea to have some reference point, when consequences of decisions motivated by current circumstances have to be evaluated.