Comparison of path-dependent functionals of semimartingales

Benedikt Köpfer; Ludger Rüschendorf

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arXiv · 1908.10076

Comparison of path-dependent functionals of semimartingales

Benedikt Köpfer·Ludger Rüschendorf

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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 Itô 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.

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Benedikt Köpfer, Ludger Rüschendorf. 2019-08-27. Comparison of path-dependent functionals of semimartingales. https://arxiv.org/abs/1908.10076

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