Comparison of path-dependent functionals of semimartingales
Benedikt K\"opfer, Ludger R\"uschendorf
TL;DR
This paper extends martingale comparison methods and functional Itô calculus to derive comparison results for path-dependent functions of semimartingales, with applications to Asian options.
Contribution
It introduces an extended Kolmogorov backward equation for path-dependent functions and provides criteria for regularity conditions in comparison theorems.
Findings
Comparison results for path-dependent functions of semimartingales
Criteria for regularity conditions in comparison theorems
Applications to Asian option pricing
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.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Risk and Portfolio Optimization