{"title":"Positivity-preserving numerical scheme for the alpha-constant elasticity of variance process","authors":"Libo Li, Guanting Liu","doi":"10.1016/j.jmaa.2025.129341","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, we present a method for constructing a positivity-preserving numerical scheme for a jump-extended constant elasticity of variance (CEV) process, where jumps are governed by a spectrally positive <em>α</em>-stable process with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>. The numerical scheme is obtained by making the diffusion coefficient <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msup></math></span>, where <span><math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, partially implicit and then finding the appropriate adjustment factor. We show that for a sufficiently small step size, the proposed scheme converges and theoretically achieves a strong convergence rate of at least <span><math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mrow><mo>(</mo><mfrac><mrow><msub><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msub></mrow><mrow><mn>2</mn></mrow></mfrac><mo>∧</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>α</mi></mrow></mfrac><mo>∧</mo><mi>ρ</mi><mo>)</mo></mrow></math></span>, where <span><math><mi>ρ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></math></span> is the Hölder exponent of the jump coefficient <span><math><msup><mrow><mi>x</mi></mrow><mrow><mi>ρ</mi></mrow></msup></math></span> and the constant <span><math><msub><mrow><mi>α</mi></mrow><mrow><mo>−</mo></mrow></msub><mo><</mo><mi>α</mi></math></span> can be chosen as arbitrarily close to <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129341"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25001222","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we present a method for constructing a positivity-preserving numerical scheme for a jump-extended constant elasticity of variance (CEV) process, where jumps are governed by a spectrally positive α-stable process with . The numerical scheme is obtained by making the diffusion coefficient , where , partially implicit and then finding the appropriate adjustment factor. We show that for a sufficiently small step size, the proposed scheme converges and theoretically achieves a strong convergence rate of at least , where is the Hölder exponent of the jump coefficient and the constant can be chosen as arbitrarily close to .
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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