This, somewhat unusual collection of problems in Measure-Theoretic Probability and Stochastic Analysis, should have been more appropriately called: ``The Problems I Like". For the material borrowed from the existing literature, full references and occasional historical remarks are provided....

We provide an alternative proof of monotonicity of normalizing volatility transforms (NVTs) due to Fukasawa (2012), and then obtain a general formula for volatility surface for which the NVTs are increasing. This is used to obtain several results related to butterfly arbitrage and asymptotic...