Volume 17, Issue 3, September 2010, Pages 281 - 292
Explicit Solution Processes for Nonlinear Jump-Diffusion Equations
Authors
Gazanfer Ünal*, †, §, Hasret Turkeri‡, ¶, Chaudry Masood Khalique*, ‖
*International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho 2735, Republic of South Africa
†Department of International Finance and Department of Mathematics, Yeditepe University, Istanbul, Turkey
‡Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
Received 18 April 2009, Accepted 7 December 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000908How to use a DOI?
- Keywords
- Compound Poisson processes; linearization conditions; stochastic integrating factor; explicit solution processes; stochastic differential equations
- Abstract
Recent studies have shown that the nonlinear jump-diffusion models give results which are in agreement with financial data. Here we provide linearization criteria together with transformations which linearize the nonlinear jump-diffusion models with compound Poisson processes. Furthermore, we introduce the stochastic integrating factor to solve the linear jump-diffusion equations. Extended Cox–Ingersoll–Ross, Brennan–Schwartz and Epstein models are shown to be linearizable and their explicit solutions are presented.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Gazanfer Ünal AU - Hasret Turkeri AU - Chaudry Masood Khalique PY - 2021 DA - 2021/01/07 TI - Explicit Solution Processes for Nonlinear Jump-Diffusion Equations JO - Journal of Nonlinear Mathematical Physics SP - 281 EP - 292 VL - 17 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000908 DO - 10.1142/S1402925110000908 ID - Ünal2021 ER -