Best upper bounds on risks altered by deductibles under incomplete information

Distribution-free option pricing

“…Therefore, we will rely on this idea and its further applications in e.g. Heijnen (1989) to derive our results.…”

A linear programming formulation for an inventory management decision problem with a service constraint

“…The equality (6) is attained when P(x) and (x À t) + are equal in both points of G. The best upper and lower bounds on this term with given moments l 1 and l 2 are derived. The method is inspired by papers of Janssen, Haezendonck, and Goovaerts (1986) and by Heijnen and Goovaerts (1989). In the following we assume the known range of the distribution to be a finite interval [a, b].…”

A simulation optimisation approach for inventory management decision support based on incomplete information

“…This section describes the method (Heijnen and Goovaerts 1989;De Schepper and Heijnen 1995) to calculate upper and lower bounds on the number of stock-out units and the stock-out probability, when only the first and second moment and the mode of the demand distribution are known.…”

“…For each case, upper and lower bounds on the number of stock-out units are determined using the results of insurance mathematics (Heijnen and Goovaerts 1989;De Vylder and Goovaerts 1982;Heijnen 1988). Next, the optimal inventory level is calculated given the desired maximum number of stock-out units.…”

“…In insurance mathematics, a lot of results have been obtained for deriving bounds on the stop-loss premium E((X − d) + ) where X is allowed to vary under some constraints such as given first order moments, unimodality etc (Heijnen and Goovaerts 1989;De Vylder and Goovaerts 1982;Heijnen 1988). A stop-loss premium limits the risk X of an insurance company to a certain amount d. Furthermore, several authors deduced bounds on tail probabilities (De Schepper and Heijnen 1995).…”