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Study of the risk-adjusted pricing methodology model with methods of geometrical analysis
Halmstad University, School of Information Technology, Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
2011 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 83, no 4-6, 333-345 p.Article in journal (Refereed) Published
Abstract [en]

Families of exact solutions are found to a nonlinear modification of the Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM) incorporates both transaction costs and the risk from a volatile portfolio. Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM equation. It gives us the possibility to describe an optimal system of subalgebras and the corresponding set of invariant solutions to the model. In this way we can describe the complete set of possible reductions of the nonlinear RAPM model. Reductions are given in the form of different second order ordinary differential equations. In all cases we provide exact solutions to these equations in an explicit or parametric form. Each of these solutions contains a reasonable set of parameters which allows one to approximate a wide class of boundary conditions. We discuss the properties of these reductions and the corresponding invariant solutions.

Place, publisher, year, edition, pages
Abingdon: Taylor & Francis, 2011. Vol. 83, no 4-6, 333-345 p.
Keyword [en]
Transaction costs, Invariant reductions, Exact solutions, Singular perturbation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-5535DOI: 10.1080/17442508.2010.489642ISI: 000299732200003Scopus ID: 2-s2.0-84859308758OAI: oai:DiVA.org:hh-5535DiVA: diva2:346568
Note

Special Issue: Optimal stopping with Applications

Available from: 2010-09-20 Created: 2010-09-01 Last updated: 2017-06-20Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf