Conference proceedings

Replication Of Wiener-Transformable Stochastic Processes With Application To Financial Markets With Memory

Year:

2018

Published in:

Stochastic Processes and their Applications
Wiener-transformable markets
adapted transformation
fractional Brownian motion
contingent claim replication
utility maximization.

We investigate Wiener-transformable markets, where the driving process is given by an adapted transformation of a Wiener process. This includes processes with long memory, like fractional Brownian motion and related processes, and, in general, Gaussian processes satisfying certain regularity conditions on their covariance functions. Our choice of markets is motivated by the well-known phenomena of the so-called “constant” and “variable depth” memory observed in real world price processes, for which fractional and multifractional models are the most adequate descriptions. Motivated by integral representation results in general Gaussian setting, we study the conditions under which random variables can be represented as pathwise integrals with respect to the driving process. From financial point of view, it means that we give the conditions of replication of contingent claims on such markets. As an application of our results, we consider the utility maximization problem in our specific setting. Note that the markets under consideration can be both arbitrage and arbitrage-free, and moreover, we give the representation results in terms of bounded strategies.

Other publications by

67 publications found

2011
Journal article

Real Harmonizable Multifractional Stable Process And Its Local Properties

Publisher: Stochastic Processes and their Applications

Authors: Georgiy Shevchenko, Marco Dozzi, Yulia Mishura, Kostiantyn Ral’chenko

2014
Working paper

Fractional Brownian Motion In A Nutshell

Publisher: arxiv

Authors: Georgiy Shevchenko

2007
Journal article

Approximation Schemes For Stochastic Differential Equations In Hilbert Space

Publisher: Theory of Probability & Its Applications

Authors: Georgiy Shevchenko, Yulia Mishura

2018
Working paper

Existence And Uniqueness Of Mild Solution To Stochastic Heat Equation With White And Fractional Noises

Publisher: arxiv

Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura

2022
Journal article

Tail Measures And Regular Variation

Publisher: Electronic Journal of Probability

Authors: Georgiy Shevchenko, Martin Bladt, Enkelejd Hashorva

2008
Journal article

The Rate Of Convergence For Euler Approximations Of Solutions Of Stochastic Differential Equations Driven By Fractional Brownian Motion

Publisher: Stochastics

Authors: Georgiy Shevchenko, Yulia Mishura

2015
Journal article

Asymptotic Behavior Of Mixed Power Variations And Statistical Estimation In Mixed Models

Publisher: Statistical Inference for Stochastic Processes

Authors: Georgiy Shevchenko, Yulia Mishura, Marco Dozzi

2011
Journal article

Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion

Publisher: Random Operators and Stochastic Equations

Authors: Georgiy Shevchenko, Yulia Mishura

2013
Journal article

Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations

Publisher: Statistics & Probability Letters

Authors: Georgiy Shevchenko, Taras Shalaiko

2016
Journal article

Stochastic Wave Equation In A Plane Driven By Spatial Stable Noise

Publisher: Modern Stochastics: Theory and Applications

Authors: Georgiy Shevchenko, Larysa Pryhara