A comparison theorem for stochastic equations of optional semimartingales

作者：Abdelghani Mohamed^*; Melnikov Alexander

来源：Stochastics and Dynamics, 2018, 18(4): 1850029.

DOI：10.1142/S0219493718500296

• Stochastic integral equations
• stochastic differential equations
• non-lipschitz condition
• optional semimartingales
• Ladlag processes
• comparison theorem
• existence and uniqueness

This paper is devoted to comparison of strong solutions of stochastic equations with respect to optional semimartingales. Optional semimartingales have right and left limits but are not necessarily continuous and therefore defined on "unusual" probability spaces. Integration theory with respect to optional semimartingales is well-developed. However, not much attention is given to stochastic integral equations of optional semimartingales. A pathwise comparison result for strong solutions of a very general class of optional stochastic equations with non-lipshitz coefficients is given. Moreover, simple applications to mathematical finance is presented.

• 出版日期2018-8