Exact and numerical solutions for two nonlinear regime switching models
*Hossein Sahebi FardCorresponding authorsahebi.hosein@shahroodut.ac.irDepartment of MathematicsFaculty of Mathematical SciencesShahrood University of TechnologyShahrood, 3619995161, Iran0000-0001-5687-4573View full profile → , Elham Dastranjelham.dastranj@shahroodut.ac.irdastranj.e@gmail.comAffiliation 1Department of MathematicsFaculty of Mathematical SciencesShahrood University of TechnologyShahrood, 3619995161, IranAffiliation 2Faculty of Mathematical SciencesUniversity of GuilanRasht, P. O. Box 41938-1914, Iran0000-0003-2545-5733View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Oct 2023
- Published Online:
- 06 Oct 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1863
- Pages:
- 2385–2398
Abstract
Keywords
Subject Classifications
References
[1] D. Bakstein and S. Howison, “A non-arbitrage liquidity model with observable parameters for derivatives,” Working Paper (2003).
[2] E. Dastranj and S. R. Hejazi, “Exact solutions for Fokker-Planck equation of geometric Brownian motion with Lie point symmetries,” Computational Methods for Differential Equations, vol. 6, no. 3, pp. 372–379 (2018).
[3] E. Dastranj and S. R. Hejazi, “New solutions for Fokker-Planck equation of special stochastic process via Lie point symmetries,” Computational Methods for Differential Equations, vol. 5, no. 1, pp. 30–42 (2017).
[4] E. Dastranj, M. R. Lotfi, R. Latifi, and A. R. Javan, “Power option pricing under the unstable conditions (evidence of power option pricing under fractional Heston model in the Iran gold market),” Physica A: Statistical Mechanics and its Applications, vol. 537, p. 122690 (2020).
[5] E. Dastranj and R. Latifi, “A comparison of option pricing models,” International Journal of Financial Engineering, vol. 4, no. 02n03, p. 1750024 (2017).
[6] E. Dastranj and H. Sahebi Fard, “Exact solutions and numerical simulation for Bakstein–Howison model,” Computational Methods for Differential Equations, vol. 10, no. 2, pp. 461–474 (2022).
[7] J. E. Esekon, “Analytic solution of a nonlinear Black–Scholes equation,” International Journal of Pure and Applied Mathematics, vol. 82, no. 4, pp. 547–555 (2013).
[8] J. E. Esekon, “A particular solution of a nonlinear Black–Scholes partial differential equation,” International Journal of Pure and Applied Mathematics, vol. 81, no. 5, pp. 715–721 (2012).
[9] S. R. Hejazi, “Lie group analysis, Hamiltonian equations and conservation laws of Born–Infeld equation,” Asian-European Journal of Mathematics, vol. 7, no. 3, p. 1450040 (2014).
[10] Y. Huang, X. Gao, C. Xu, and H. Liang, “Space-time spectral collocation method for solving Burgers equations with the convergence analysis,” Symmetry, vol. 11, no. 12, p. 1439 (2019).
[11] E. Lashkarian, S. R. Hejazi, N. Habibi, and A. Motamednezhad, “Symmetry properties, conservation laws, reduction and numerical approximations of time-fractional cylindrical-Burgers equation,” Computational Methods for Differential Equations, vol. 10, no. 4, pp. 655–669 (2022).
[12] H. Sahebi Fard, E. Dastranj, and A. Abdolbaghi Ataabadi, “Analytical and numerical solutions for the pricing of a combination of two financial derivatives in a market under Hull–White model,” Advances in Mathematical Finance and Applications, vol. 7, no. 4, pp. 1013–1023 (2022).
[13] H. Sahebi Fard, E. Dastranj, R. Hejazi, and A. Jajarmi, “Analytical and numerical solutions for a special nonlinear equation,” International Journal of Financial Engineering, vol. 11, no. 1, p. 2350057 (2024).
[14] J. Shen, T. Tang, and L. L. Wang, Spectral Methods: Algorithms, Analysis and Applications, vol. 41. Berlin, Germany: Springer Science & Business Media (2011).
