The reinsurance to be treated in this note shall cover the excess over a certain limit Q of the total amount of claims for each accounting period paid by the ceding company. Regardless of the rule for the determination of the limit Q such a reinsurance shall in this context be called stop loss reinsurance.

Generally, such a reinsurance is called either stop loss or excess of loss reinsurance depending on the rule for the determination of Q. The use of the term stop loss regardless of this rule is preferred here in order to avoid confusion with an excess of loss reinsurance which refers to the excess of the amount of one or more claims caused by an individual event.

The total amount of claims paid by the ceding company c during the period t shall be denoted cXt. This random function constitutes for a fixed value of c a stochastic process with the discontinuous parameter t > o.

(It may be remarked that for a fixed pair of values of c and tcXt can be regarded as a particular value of a sample function pertaining to the process of the continuous paramater τ generally considered in the collective theory of risk to which the total amount of claims up to time τ is attached, in this case o < τ ≤ 1. cXt can also be considered as the increments during the time interval t of the total amount of the claims up to τ.)