9.7 The impact of individual policy modifications on aggregate payments

In Section 8.6 the manner in which individual deductibles (both ordinary and franchise) affect both the individual loss amounts and the claim frequency distribution is discussed. In this section we consider the impact on aggregate losses. It is worth noting that both individual coinsurance and individual policy limits have an impact on the individual losses but not on the frequency of such losses, so we focus primarily on the deductible issues in what follows. We also remark that we continue to assume that the presence of policy modifications does not have an underwriting impact on the individual loss distribution through an effect on the risk characteristics of the insured population, an issue discussed in Section 8.6. That is, the ground-up distribution of the individual loss amount X is assumed to be unaffected by the policy modifications, and only the payments themselves are affected.

From the standpoint of the aggregate losses, the relevant facts are now described. Regardless of whether the deductible is of the ordinary or franchise type, we shall assume that an individual loss results in a payment with probability v. The individual ground-up loss random variable X has policy modifications (including deductibles) applied, so that a payment is then made. Individual payments may then be viewed on a per-loss basis, where the amount of such payment, denoted by YL, will be zero if the loss results in no payment. ...

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