A comparison theorem for stochastic equations of optional semimartingales-Reference-Cited by-同舟云学术

A comparison theorem for stochastic equations of optional semimartingales

Published:2018-08 Issue:04 Volume:18 Page:1850029
ISSN:0219-4937
Container-title:Stochastics and Dynamics
language:en
Short-container-title:Stoch. Dyn.

Author:

Abdelghani Mohamed¹,Melnikov Alexander²

Affiliation:

1. Machine Learning Group, Morgan Stanley, 750 7th Ave, New York City, NY 10019, USA

2. Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G-2G1, Canada

Abstract

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.

Funder

Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada

Publisher

World Scientific Pub Co Pte Lt

Subject

Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219493718500296

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