  This archiving article consists of several short reports on the discussions
between the two authors over the past two years at Oxford and Madrid, and their
work carried out during that period on the upper bound of the Kullback-Leibler
divergence and cross entropy. The work was motivated by the cost-benefit ratio
proposed by Chen and Golan [1], and the less desirable property that the
Kullback-Leibler (KL) divergence used in the measure is unbounded. The work
subsequently (i) confirmed that the KL-divergence used in the cost-benefit
ratio should exhibit a bounded property, (ii) proposed a new divergence
measure, and (iii) compared this new divergence measure with a few other
bounded measures.
