
289From Costing to Pricing
b. R is monotonic, that is, if in all possible outcomes the losses from one portfolio S
1
are smaller than the losses from another portfolio S
2
(i.e. S
1
≤ S
2
), then* R(S
1
) ≤ R(S
2
).
If this were not the case, one could think of decreasing one’s risk by writing more business!
c. R is positive-homogeneous: if α > 0, R(αS
1
) = αR(S
1
), that is, doubling (halving) one’s
share in a portfolio of risks simply results in twice (half) the risk.
Note that increasing the portfolio in this way does not bring any diversication benet
because the added risk is perfectly correlated with the existing one. An example is provided