The coupon

The Coupon Report

The Coupon Collector’s Problem

In this note we will consider the following problem: how many coupons we have to purchase (on average) to complete a collection. This problem, which takes everybody back to his childhood when this was really “a problem”, has been considered by the probabilists since the eighteenth century and nowadays it is still possible to derive some new results, probably original or at least never published...

Coupon Collecting

We consider the classical coupon collector’s problem in which each new coupon collected is type i with probability pi; P i1⁄41 n pi1⁄41. We derive some formulas concerning N, the number of coupons needed to have a complete set of at least one of each type, that are computationally useful when n is not too large. We also present efficient simulation procedures for determining P(N . k), as well a...

The Coupon Subset Collection Problem

The coupon subset collection problem is a generalization of the classical coupon collecting problem, in that rather than collecting individual coupons we obtain, at each time point, a random subset of coupons. The problem of interest is to determine the expected number of subsets needed until each coupon is contained in at least one of these subsets. We provide bounds on this number, give effic...

Risky coupon bonds as a portfolio of zero-coupon bonds

This paper characterizes conditions under which a risky coupon bond is equivalent to a portfolio of risky zero-coupon bonds. This characterization is extended to enable the estimation of firm specific zero-coupon bond prices from risky coupon bond prices for the determination of firm specific credit risk curves.  2004 Elsevier Inc. All rights reserved.