Existence of solutions of some boundary value problems with stochastic volatility
This paper aims at obtaining the analytical solutions of some boundary value problems garnished with stochastic volatility, price volatility risk and the risk premium. A set of functions is constructed which transforms the problem into a Laplace equation and a heat equation. The analytical solutions...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-02-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844020302668 |
| _version_ | 1818057449549070336 |
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| author | B.O. Osu E.O. Eze U.E. Obasi H.I. Ukomah |
| author_facet | B.O. Osu E.O. Eze U.E. Obasi H.I. Ukomah |
| author_sort | B.O. Osu |
| collection | DOAJ |
| description | This paper aims at obtaining the analytical solutions of some boundary value problems garnished with stochastic volatility, price volatility risk and the risk premium. A set of functions is constructed which transforms the problem into a Laplace equation and a heat equation. The analytical solutions of these equations are obtained. Then existence of a unique solution is achieved which represents the behavior of volatile behavior of the system. Some numerical illustration of the models is obtained using the Maple software. |
| first_indexed | 2024-12-10T12:44:55Z |
| format | Article |
| id | doaj.art-d64fc4b6fdac43abb676d5ebabbab942 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-12-10T12:44:55Z |
| publishDate | 2020-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-d64fc4b6fdac43abb676d5ebabbab9422022-12-22T01:48:26ZengElsevierHeliyon2405-84402020-02-0162e03421Existence of solutions of some boundary value problems with stochastic volatilityB.O. Osu0E.O. Eze1U.E. Obasi2H.I. Ukomah3Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria; Corresponding author.Department of Mathematics, Michael Okpara University of Agriculture, Umudike, NigeriaDepartment of Mathematics, Michael Okpara University of Agriculture, Umudike, NigeriaDepartment of Mathematics, Abia State University, Uturu, NigeriaThis paper aims at obtaining the analytical solutions of some boundary value problems garnished with stochastic volatility, price volatility risk and the risk premium. A set of functions is constructed which transforms the problem into a Laplace equation and a heat equation. The analytical solutions of these equations are obtained. Then existence of a unique solution is achieved which represents the behavior of volatile behavior of the system. Some numerical illustration of the models is obtained using the Maple software.http://www.sciencedirect.com/science/article/pii/S2405844020302668Computational mathematicsFinancial BVPStochastic volatilityHeat equationLaplace equation |
| spellingShingle | B.O. Osu E.O. Eze U.E. Obasi H.I. Ukomah Existence of solutions of some boundary value problems with stochastic volatility Heliyon Computational mathematics Financial BVP Stochastic volatility Heat equation Laplace equation |
| title | Existence of solutions of some boundary value problems with stochastic volatility |
| title_full | Existence of solutions of some boundary value problems with stochastic volatility |
| title_fullStr | Existence of solutions of some boundary value problems with stochastic volatility |
| title_full_unstemmed | Existence of solutions of some boundary value problems with stochastic volatility |
| title_short | Existence of solutions of some boundary value problems with stochastic volatility |
| title_sort | existence of solutions of some boundary value problems with stochastic volatility |
| topic | Computational mathematics Financial BVP Stochastic volatility Heat equation Laplace equation |
| url | http://www.sciencedirect.com/science/article/pii/S2405844020302668 |
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