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  • 1.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Convergence of American knock out options in discrete time.2010Report (Other academic)
  • 2.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Convergence of Option Rewards2010Doctoral 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.

  • 3.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Optimal Stopping and Convergence of Option Rewards2009Licentiate 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.

  • 4.
    Lundgren, Robin
    Mälardalen University, Department of Mathematics and Physics.
    Optimal Stopping Domains for Discrete Time Knock Out American Options2007In: Recent Advances in Stochastic Modelling and Data Analysis: Chania, Greece, 29 May - 1 June 2007, World Scientific , 2007, p. 613-620Chapter in book (Refereed)
  • 5.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Simulation studies of stopping domains for American knock out optionsIn: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171Article in journal (Refereed)
  • 6.
    Lundgren, Robin
    Mälardalen University, Department of Mathematics and Physics.
    Structure of Optimal Stopping Domains for American Options with Knock out Domains2007In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 13(29), no 4, p. 98-129Article in journal (Refereed)
    Abstract [en]

    American options give us the possibility to exercise them at any moment of time up to maturity. An optimal stopping domain for American type options is a domain that, if the underlying price process enters we should exercise the option. A knock out option is a American barrier option of knock out type, but with more general shape structure of the knock out domain. An algorithm for generating the optimal stopping domain for American type knock out options is constructed. Monte Carlo simulation is used to determine the structure of the optimal stopping domain. Results of the structural, and stability of studies are presented for different models of payoff functions and knock out domains.

  • 7.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Convergence and Approximation of Option Rewards for Multivariate Price Processes2009Report (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.

  • 8.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Optimal stopping and reselling of European options2010In: 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. 

  • 9.
    Lundgren, Robin
    et al.
    Mälardalen University, School of Education, Culture and Communication.
    Silvestrov, Dmitrii
    Mälardalen University, School of Education, Culture and Communication.
    Kukush, Alexander
    Kiev University.
    Reselling of options and convergence of option rewards2008In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 30, no 3-4Article in journal (Refereed)
    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

  • 10.
    Silvestrov, Dmitrii
    et al.
    Stockholm University.
    Lundgren, Robin
    Mälardalen University, School of Education, Culture and Communication.
    Convergence of option rewards for multivariate price processes2013In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 85, p. 53p. 115-131Article in journal (Refereed)
    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.

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