Moment Bounds for Truncated Bimodal Distributions
Guoqing Liu, Minhui Wang · Journal of Natural Science of Heilongjiang University · 2011
Given any bimodal random variable X(subscript ∈) with EX(superscript i)=m(subscript i)(i=1, 2, 3) and modes fixed, upper bounds are derived on small value probability P(X≤t) and the truncated random variable max (0, X-K) with K＞0 given. Motivation comes not only from small value probability but also from questions associated with European call option under mixture of two unimodal distribution. The key techniques are to pass the distribution function to an auxiliary function and then to employ duality theory and change of measures.