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Convergence of option rewards for multivariate price processes
Stockholm University.ORCID iD: 0000-0002-2626-5598
Mälardalen University, School of Education, Culture and Communication.
2013 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 85, p. 53p. 115-131Article in journal (Refereed) Published
Abstract [en]

American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes.Convergence results areobtained for optimal reward functionals of American type options forperturbed multivariate Markov processes. Theseresults are applied to approximation tree type algorithms forAmerican type options for exponential diffusion type price processes.Application to mean-reverse price processes used to model stochasticdynamics of energy prices are presented. Also application to reselling of European options are given.

Place, publisher, year, edition, pages
2013. Vol. 85, p. 53p. 115-131
Keywords [en]
American option; Convergence of option rewards; binomial-trinomial tree approximation; optimal stopping; skeleton approximation; multivariate Markov price process
National Category
Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-8064DOI: 10.1090/S0094-9000-2013-00879-5Scopus ID: 2-s2.0-84877857656OAI: oai:DiVA.org:mdh-8064DiVA, id: diva2:293289
Available from: 2010-02-11 Created: 2010-02-11 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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Silvestrov, Dmitrii

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Citation style
  • apa
  • ieee
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  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf