Fu and Khury (2011)note that with in a variance framework, both desirable (e.g., smaller than expected
claim payments) and undesirable variations increase risk.
An insurer, however, is only concerned with larger than expected claim payments
as such loss events place a sprain on retained capital and reserves, and
increase the probability of ruin (Fishburn, 1977).
As such,Fishburn (1977)suggested using“lower partial moment”(LPM) instead of the
total variance as the risk measure.
For insurance claims, LPM takes the following form: