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....

This paper addresses the problem of specifying boundary conditions for Fokker-Planck PDE for reflecting diffusions arising in finance. Main focus is the CIR model, but techniques presented are readily applicable to other models with reflecting boundaries

We look at the real positive (semi)definite matrix completion problem from the convex optimization viewpoint.The problem is introduced via relative entropy minimization, transformed into the standard max-det from, and conditions are sought for existence of positive definite and positive...

We revisit the classical problem of convergence of the maximum of cumulative sums of IID random variables by introducing ideas from the Karamata's celebrated proof of the Hardy-Littlewood Tauberian Theorem [J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes,...

We revisit the problem addressed in Gatarek et al. and derive an algorithm for determining the Chayette local volatility based on the options marked for fixed-tenor rolling maturity swaptions. Apart from the discretization error inherent in calibration-simulation procedures, the formula...

Motivated by the recent Log Moment formula of \cite{raval_jacquier21}, we look at the power of absolute Log Contract $|\log(S_T/F_T)|^q$, $q\geq 1$, and derive its corresponding replicating strip of Vanilla options. Unlike the standard Log Contract where the Delta of the replicating portfolio...

At present, the most liquidly traded listed options on the crypto underlying are so-called inverse vanilla options. In this note we show how such contacts are just regular vanilla options considered under the well-known martingale measure making underlying the numeraire