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Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem.

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Title: Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem.
Authors: Pascucci, A.1 andrea.pascucci@unibo.it, Suárez-Taboada, M.2 mariasuarez@udc.es, Vázquez, C.2 carlosv@udc.es
Source: Journal of Mathematical Analysis & Applications. Jul2013, Vol. 403 Issue 1, p38-53. 16p.
Subjects: Mathematical analysis, Numerical analysis, Partial differential equations, Pricing, Stocks (Finance), Kolmogorov complexity, Polynomials
Abstract: Abstract: In this paper the mathematical analysis of a model for pricing stock loan contracts, when the accumulative dividend yield associated to the stock is returned by the lender to the borrower on redemption, is carried out. More precisely, the model is formulated in terms of an obstacle problem associated to a Kolmogorov equation and the existence and uniqueness in the set of solutions with polynomial growth are obtained. Also some regularity properties of the solution are analyzed. Next, for the numerical solution of the problem the combination of Crank–Nicolson Lagrange–Galerkin with the augmented Lagrangian active set method is described. Finally, some numerical examples illustrate the theoretical properties of the optimal redeeming boundary previously stated in the literature. [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 88978484
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PubTypeId: academicJournal
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  Data: Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem.
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  Data: Abstract: In this paper the mathematical analysis of a model for pricing stock loan contracts, when the accumulative dividend yield associated to the stock is returned by the lender to the borrower on redemption, is carried out. More precisely, the model is formulated in terms of an obstacle problem associated to a Kolmogorov equation and the existence and uniqueness in the set of solutions with polynomial growth are obtained. Also some regularity properties of the solution are analyzed. Next, for the numerical solution of the problem the combination of Crank–Nicolson Lagrange–Galerkin with the augmented Lagrangian active set method is described. Finally, some numerical examples illustrate the theoretical properties of the optimal redeeming boundary previously stated in the literature. [Copyright &y& Elsevier]
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  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.jmaa.2013.02.007
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      – Code: eng
        Text: English
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        PageCount: 16
        StartPage: 38
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        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Partial differential equations
        Type: general
      – SubjectFull: Pricing
        Type: general
      – SubjectFull: Stocks (Finance)
        Type: general
      – SubjectFull: Kolmogorov complexity
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      – SubjectFull: Polynomials
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      – TitleFull: Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem.
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              M: 07
              Text: Jul2013
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              Y: 2013
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