Comparison of path-dependent functionals of semimartingales
Probability
2019-08-28 v1
Abstract
Based on an extension of the martingale comparison method some comparison results for path-dependent functions of semimartingales are established. The proof makes essential use of the functional It\^o calculus. A main tool is an extension of the Kolmogorov backwards equation to path-dependent functions. The paper also derives criteria for the regularity conditions of the comparison theorems and discusses applications as to the comparison of Asian options for semimartingale models.
Cite
@article{arxiv.1908.10076,
title = {Comparison of path-dependent functionals of semimartingales},
author = {Benedikt Köpfer and Ludger Rüschendorf},
journal= {arXiv preprint arXiv:1908.10076},
year = {2019}
}