Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models
The main purpose of this work is to establish a new links between the stochastic Cox-Ingersoll-Ross (CIR) model and the stochastic Rayleigh diffusion process (SRDP) and the links between the Vasicek Interest Rate (VIR) process and the stochastic Gompertz diffusion process (SGDP). These links focus o...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EJAAM
2023-12-01
|
| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2023/10.62780-ejaam-2023-001.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823864924223307776 |
|---|---|
| author | Abdenbi El Azri Ahmed Nafidi |
| author_facet | Abdenbi El Azri Ahmed Nafidi |
| author_sort | Abdenbi El Azri |
| collection | DOAJ |
| description | The main purpose of this work is to establish a new links between the stochastic Cox-Ingersoll-Ross (CIR) model and the stochastic Rayleigh diffusion process (SRDP) and the links between the Vasicek Interest Rate (VIR) process and the stochastic Gompertz diffusion process (SGDP). These links focus on elementary stochastic calculus and Itô’s calculus. Firstly, we prove that the square root of the CIR model is a SRDP. Secondly, we prove that the square of the SRDP is a CIR model. Thirdly, we prove that the exponential of the VIR model is a SGDP. Finally, we prove that the logarithm of the SGDP is a VIR model. New computations of the probability transition density function (PTDF) and the trend functions of the processes have quite simple formulations |
| format | Article |
| id | doaj-art-c107f6606e5c4954b80e0cf54420322c |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-c107f6606e5c4954b80e0cf54420322c2025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902023-12-01202310.62780/ejaam/2023-001Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion modelsAbdenbi El Azri0Ahmed Nafidi1Hassan First University of Settat, National School of Applied Sciences, B.P. 218, 26103 Berrechid, MoroccoHassan First University of Settat, National School of Applied Sciences, B.P. 218, 26103 Berrechid, MoroccoThe main purpose of this work is to establish a new links between the stochastic Cox-Ingersoll-Ross (CIR) model and the stochastic Rayleigh diffusion process (SRDP) and the links between the Vasicek Interest Rate (VIR) process and the stochastic Gompertz diffusion process (SGDP). These links focus on elementary stochastic calculus and Itô’s calculus. Firstly, we prove that the square root of the CIR model is a SRDP. Secondly, we prove that the square of the SRDP is a CIR model. Thirdly, we prove that the exponential of the VIR model is a SGDP. Finally, we prove that the logarithm of the SGDP is a VIR model. New computations of the probability transition density function (PTDF) and the trend functions of the processes have quite simple formulationshttps://ejaam.org/articles/2023/10.62780-ejaam-2023-001.pdfcox-ingersoll-ross modelrayleigh diffusion processvasicek interest rate modelstochastic gompertz diffusion process |
| spellingShingle | Abdenbi El Azri Ahmed Nafidi Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models E-Journal of Analysis and Applied Mathematics cox-ingersoll-ross model rayleigh diffusion process vasicek interest rate model stochastic gompertz diffusion process |
| title | Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models |
| title_full | Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models |
| title_fullStr | Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models |
| title_full_unstemmed | Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models |
| title_short | Some remarks on the links between the VIR and Gompertz diffusion models and the links between the CIR and Rayleigh diffusion models |
| title_sort | some remarks on the links between the vir and gompertz diffusion models and the links between the cir and rayleigh diffusion models |
| topic | cox-ingersoll-ross model rayleigh diffusion process vasicek interest rate model stochastic gompertz diffusion process |
| url | https://ejaam.org/articles/2023/10.62780-ejaam-2023-001.pdf |
| work_keys_str_mv | AT abdenbielazri someremarksonthelinksbetweenthevirandgompertzdiffusionmodelsandthelinksbetweenthecirandrayleighdiffusionmodels AT ahmednafidi someremarksonthelinksbetweenthevirandgompertzdiffusionmodelsandthelinksbetweenthecirandrayleighdiffusionmodels |