Arnold, Crack and Schwartz (ACS) (2010) generalize the Rubinstein (1994) risk-neutral implied binomial tree (R-IBT) model by introducing a risk premium. Their new risk-averse implied binomial tree model (RA-IBT) has both probabilistic and pricing applications. They use the RA-IBT model to...

Karl Pearson's chi-squared test is widely known and used, both as a goodness-of-fit test for hypothesized distributions or frequencies, and in tests of independence in contingency tables. The test was introduced in Pearson (1900), but the derivation in that paper is almost incomprehensible. Two...

We use the Lindberg-Levy central limit theorem (CLT), Tchebychev's inequality, Slutsky's theorem, and general rules for limiting distributions to demonstrate sufficient conditions under which the Student-t test statistic for the mean is asymptotically standard normal. Although there exist weaker...