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Optimal stopping and reselling of European options
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.ORCID iD: 0000-0002-2626-5598
2010 (English)In: Mathematical and Statistical Models and Methods in Reliability / [ed] Rykov, V., Balakrishan, N., Nikulin, M, Boston: Birkhäuser , 2010Chapter in book (Refereed)
Abstract [en]

We consider the problem of optimal reselling of European options. A bivariate exponential diffusion process is used to describe the reselling model. In this way, the reselling problem is imbedded to the model of finding optimal reward for American type option based on this process. Convergence results are formulated for optimal reward functionals of American type options for perturbed multi-variate Markov processes. An approximation bivariate tree model is constructed and convergence of optimal expected reward for this tree model to the optimal expected reward for the corresponding reselling model is proved. 

Place, publisher, year, edition, pages
Boston: Birkhäuser , 2010.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-10283DOI: 10.1007/978-0-8176-4971-5_29ISI: 000292954700029ISBN: 978-0-8176-4970-8 (print)OAI: oai:DiVA.org:mdh-10283DiVA: diva2:350078
Available from: 2010-09-09 Created: 2010-09-09 Last updated: 2015-01-30Bibliographically approved
In thesis
1. Convergence of Option Rewards
Open this publication in new window or tab >>Convergence of Option Rewards
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of an introduction and five articles devoted to optimal stopping problems of American type options. In article A, we get general convergence results for the American option rewards for multivariate Markov price processes. These results are used to prove convergence of tree approximations presented in papers A, B, C and E.In article B, we study the problem of optimal reselling for European options. The problem can be transformed to the problem of exercising an American option with two underlying assets. An approximative binomial-trinomial tree algorithm for the reselling model is constructed. In article C, we continue our study of optimal reselling of European options and give the complete solution of the approximation problem. In the article D, we consider general knockout options of American type. A Monte-Carlo method is used to study structure of optimal stopping domains generated by combinations of different pay-off functions and knockout domains.In article E the American option with knock out domains is considered. In order to show convergence of the reward functional the problem is reformulated in such a way that the convergence results in paper A can be applied.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2010
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 89
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-10327 (URN)978-91-86135-84-3 (ISBN)
Public defence
2010-11-12, Kappa, Högskoleplan 1, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2010-09-22 Created: 2010-09-21 Last updated: 2010-10-21Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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  • text
  • asciidoc
  • rtf