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Optimal Stopping and Convergence of Option Rewards
Mälardalen University, School of Education, Culture and Communication. (Avdelningen för tillämpad matematik)
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is based on two articles devoted to optimal stopping problems of American type options.

In article A, 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. An approximate binomial-trinomial tree algorithm for the reselling model is constructed.

In article B, 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 and B.

Place, publisher, year, edition, pages
2009. , p. 150
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 101
Identifiers
URN: urn:nbn:se:mdh:diva-5637ISBN: 978-91-86135-21-8 (print)OAI: oai:DiVA.org:mdh-5637DiVA, id: diva2:209045
Presentation
2009-04-23, Gamma, Högskoleplan 1, hus U, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2009-03-24 Created: 2009-03-23 Last updated: 2015-01-30Bibliographically approved
List of papers
1. Convergence and Approximation of Option Rewards for Multivariate Price Processes
Open this publication in new window or tab >>Convergence and Approximation of Option Rewards for Multivariate Price Processes
2009 (English)Report (Other (popular science, discussion, etc.))
Abstract [en]

Multivariate Markov price processes and American type options for such processes with generalpayoff functions with not more than polynomial rate of growth are considered. Convergence results are obtainedfor optimal reward functionals of American type options for perturbed multivariateMarkov processes and payoff functions. These results are applied to approximation tree type algorithmsfor American type options for exponential diffusion type priceprocesses including mean-reverse stochastic processesused to model stochastic dynamics of energy prices.

Publisher
p. 46
Series
Research Reports MDH/UKK, ISSN 1404-4978 ; 2009-1
Keywords
American option, Reward, Convergence, 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:nbn:se:mdh:diva-5636 (URN)
Available from: 2009-03-23 Created: 2009-03-23 Last updated: 2015-01-30Bibliographically approved
2. Reselling of options and convergence of option rewards
Open this publication in new window or tab >>Reselling of options and convergence of option rewards
2008 (English)In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 30, no 3-4Article in journal (Refereed) Published
Abstract [en]

We consider the problem of optimal reselling of Europeanoptions. A bivariate exponential diffusion process is used todescribe the reselling model. In this way, the reselling problem isimbedded to the model of finding optimal reward for American typeoption based on this process. Convergence results are obtained foroptimal reward functionals of American type options for perturbedmulti-variate Markov processes. An approximation  bivariate treemodel is constructed and convergence of optimal expected reward forthis tree model to the optimal expected reward for the correspondingAmerican type option is proved

Keywords
European option, reselling problem, American option, reward convergence, optimal stopping, skeleton approximation, Markov process, binomial-trinomial approximation.
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-5083 (URN)
Available from: 2009-02-10 Created: 2009-02-10 Last updated: 2017-02-15Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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  • Other locale
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Output format
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