Topic: Stopping Times and the Optional Stopping Theorem

Optional Sampling for Submartingales and Supermartingales

One-Sided Ruin and the Limits of Optional Stopping

Measurability of Stopped Values

Hitting Times and First-Entry Rules

Fair Gambler’s Ruin with Two Absorbing Barriers

Expected Time to the Kth Poisson Arrival

Expected Exit Time from a Finite Random-Walk Interval

Dominating Bounds That Guarantee Uniform Integrability

Diagnosing Optional Stopping Hypotheses

Counterexamples to Unrestricted Optional Stopping