On comparison theorem for optional SDEs via local times and applications. Issue 3 (3rd April 2022) - Abdelghani, Mohamed; Melnikov, Alexander; Pak, Andrey
Abstract : In this paper, we study SDEs with respect to optional semimartingales or optional SDEs. Our leading idea is to explore the concept and technique of local time of optional processes to extend several results on comparison and pathwise uniqueness of solutions of such stochastic equations. We also obtain a comparison result for optional stochastic equations with different jump-diffusions. Moreover, we apply our comparison theorem to calculate option price bounds in mathematical finance. Our findings are supported by numerical examples.