Dynamic optimal reinsurance for stochastic catastrophe with dependent claim risks
An adjustable reinsurance model for stochastic catastrophe was established under the conditions that the claim risks are time-varying and dependent.On the basis of showing the optimality of excess-of-loss reinsurance treaty,discussions found that the objective functions under arbitrary dependence structure are decreasing first and then turn out to be increasing as the retention level of catastrophe risk increases,thus the explicit expression of the retention vector was given in a general form.According to the characteristic of catastrophe risks,the retention vector under a particular dependence structure was further presented as well and a concrete example was studied to optimize the expected utility or variance of the retained risks.The result shows that both the satisfaction of reinsurance and the stability of business reduce as the dependence intensity of catastrophe risks increase,the negative effect to the insurer is very obvious.Meanwhile,to optimize the objects of reinsurance with objective risks,the risk retention level in usual case shall also rise up,which reflects the superiority of dynamic reinsurance.
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