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

Log-supermodularity of weight functions and the loading monotonicity of weighted insurance premiums