  The paper is motivated by a problem concerning the monotonicity of insurance
premiums with respect to their loading parameter: the larger the parameter, the
larger the insurance premium is expected to be. This property, usually called
loading monotonicity, is satisfied by premiums that appear in the literature.
The increased interest in constructing new insurance premiums has raised a
question as to what weight functions would produce loading-monotonic premiums.
In this paper we demonstrate a decisive role of log-supermodularity in
answering this question. As a consequence, we establish - at a stroke - the
loading monotonicity of a number of well-known insurance premiums and offer a
host of further weight functions, and consequently of premiums, thus
illustrating the power of the herein suggested methodology for constructing
loading-monotonic insurance premiums.
