where z is the maximum acceptable claim payment (which can indicate the maximum acceptable loss rate, the average claim payment, below average claim payments, depending on the insurer's risk perception), mis a measure of risk perception sensitivity to large loss, and F(m) is the probability function of m.
Unlike the total variance, LPM only measures variation above z.
When α= 2, the LPM is called the semi-variance (e.g., see Fu & Khury, 2011). Therefore, the semi-variance can
be defined as