Stopping Times and Stopped Processes

📐 Research in Stochastic Processes: Stopping Times and Stopped Processes

📄 Stopping Times and Stopped Processes

This research, completed at my senior year, provides a rigorous exploration of stopping times and stopped processes in discrete-time probability spaces. Under the supervision of Prof. Vahagn Nersesyan, we formalized the equivalence definitions of stopping times, examined stopping rules in a two-period binary market, and constructed counterexamples that require future information—thus violating the definition.

The report further introduces the concept of stopped processes, derives their representations, and proves that the stopped version of a (super/sub)martingale retains its respective properties. Proofs include decomposition via indicator functions and expectations under filtration, illustrating the core principles behind optional stopping theorems.