Title: Moment bounds for truncated random variables.
Bounds involving moments of random variables arise naturally in
many areas of probability, statistics, economics, and operations research.
There is also a long history of studying them, back to works of Chebyshev.
We first review and update some optimal bounds on the probability
that a bounded random variable belongs in a set, given some of its moments.
Then we present some new bounds on the expectation and variance
of truncated random variable, motivated by works on European call option.
