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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Convergence of option rewards for multivariate price processes


Authors: D. S. Silvestrov and R. Lundgren
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 115-131
MSC (2000): Primary 60J05, 60H10; Secondary 91B28, 91B70
Published electronically: January 14, 2013
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Abstract: American type options with general payoff functions possessing polynomial rate of growth are considered for multivariate Markov price processes. Convergence results for optimal reward functionals of American type options for perturbed multivariate Markov processes are presented. These results are applied to approximation tree type algorithms for American type options for exponential multivariate Brownian price processes and mean-reverse price processes used to model stochastic dynamics of energy prices.


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Additional Information

D. S. Silvestrov
Affiliation: Stockholm University, Sweden
Email: silvestrov@math.su.se

R. Lundgren
Affiliation: Mälardalen University, Västerås, Sweden
Email: robin.lundgren@mdh.se

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00879-5
PII: S 0094-9000(2013)00879-5
Keywords: Reward, convergence, optimal stopping, American option, skeleton approximation, Markov type price process, exponential multivariate Brownian price process, mean-reverse price process
Received by editor(s): April 4, 2011
Published electronically: January 14, 2013
Additional Notes: The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held on September 7–11, 2010 at Kyiv National Taras Shevchenko University and dedicated to three anniversaries of prominent Ukrainian scientists: AnatoliI SkoroKhod, Volodymyr Korolyuk and Igor Kovalenko
Article copyright: © Copyright 2013 American Mathematical Society