Abstract
Given any random variable X ∈ [ 0 , M ] with E X = m 1 and E X 2 = m 2 fixed, various bounds are derived on the mean and variance of the truncated random variable max ( 0 , X − K ) with K > 0 given. The results are motivated by questions associated with European call options. The techniques are based on domination by quadratic functions and change of measures in the unimodal distribution case.
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