International Journal of Nonlinear Analysis and Applications

Change of measure in fractional stochastic differential equation

Document Type : Research Paper

Authors

1 Universirty of Al-Qadisiyah, Iraq

2 {Universirty of Al-Qadisiyah, Iraq

Abstract

Change of measure is a very well known common criterion in both the probability rules and applications. The change of measure is a transformation from actual measure to equivalent measure. We will employ the change of measure in Fractional Stochastic Differential Equations (FSDE), which is a general form of Stochastic Differential Equation (SDE). We will implement our method to some important examples, like, Fractional Brownian Motion (FBM) and Fractional Levy process (FL).

Keywords

[1] M.F. Al-Saadony and W.J. Al-Obaidi, Estimation the vasicek interest rate model driven by fractional L´evy processes with application, J. Phys. Conf. Ser. 1897(1) (2021) 012017.
[2] D. Applebaum, Le’vy Processes and Stochastic Calculus, Second Edition, Cambridge University Press, 2009.
[3] O.E. Barndorff-Nielsen and A. Shiryrov, Change of Time and Change of Measure, Volume 15 of Advanced Series
on Statistical Science and Applied Probability, (Second ed.) World Scientific Publishing, 2015.
[4] F. Biagini, Y. Hu, B. Øksendal and T. Zhang, Stochastic Calculus for Fractional Brownian Motion and Applications, Springer, London, 2006.
[5] P.J.E. Hunt, Financial Derivatives in Theory and Practice, Wiley Series in Probability and Statistics, Revised
Edition, Wiley Publishing, 2005.
[6] S.M. Iacus, Option Pricing and Estimation of Financial Models with R, (First ed.), John Wiley & Sone Italy,
2011.
[7] S.M. Iacus, Simulation and Inference for Stochastic Differential Equations with R Examples, (First ed.), Springer
Italy, 2008.
[8] F.C. Klebaner, Introduction to Stochastic Calcites with Applications, (Third ed.), Imperial College Press, Australia, 2012.
[9] T. Marquardi and C. Bender. Stochastic calculus for convoluted Le’vy process, Bernoulli 14(2) (2018) 499–518.
[10] T. Marquardi, Fractional Le’vy process with an application to long moniery moving average processes, Bernardli
12(6) (2006) 1099–1126.
[11] T. Mikosch, Elementary Stochastic Calcites with Finance in View. Volume 6 of Advanced Series on Statistical
Science and Applied Probability, World Scientific Publishing, 1998.
[12] T. Mikosch, Elementary Stochastic Calculus, (5th ed.), World Scientific Publishing, 2004.
[13] Y. Miyahara, Option Pricing in Incomplete Markets: Modeling Based on Geometric Le’vy Processes and Minimal
Entropy Martingale Measures, Quanutative Finance, World Scientific, Imperial College Press, 2012.
[14] T. Rheinander and J. Sexton, Hedging Derivatives, Advanced Series on Statistical Science and Applied Probability,
World Scientific Publishing, 2011.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 3475-3478
  • Receive Date: 10 September 2021
  • Revise Date: 27 October 2021
  • Accept Date: 13 November 2021