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Theory of Probability and Mathematical Statistics

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Functional limit theorems for stochastic integrals with applications to risk processes and to self-financing strategies in a multidimensional market. I


Authors: Yu. S. Mishura, G. M. Shevchenko and Yu. V. Yukhnovs’kiĭ
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 81 (2010).
Journal: Theor. Probability and Math. Statist. 81 (2010), 131-146
MSC (2010): Primary 60G44, 60F05, 60B12
Published electronically: January 20, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: We study sufficient conditions for the weak convergence of stochastic integrals with respect to processes of bounded variation, martingales, or semimartingales. A semimartingale theorem is extended to the multidimensional case. We apply a limit procedure and pass from processes of bounded variation to risk processes. An "inverse" problem for the weak convergence is also considered.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: zhora@univ.kiev.ua

Yu. V. Yukhnovs’kiĭ
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: Yuhnovskiy@hq.eximb.com

DOI: https://doi.org/10.1090/S0094-9000-2011-00815-0
Keywords: Stochastic integrals, functional limit theorems, weak convergence, semimartingales
Received by editor(s): July 10, 2009
Published electronically: January 20, 2011
Additional Notes: The first two authors are grateful to the European Commissions for support in the framework of the program “Marie Curie Actions”, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2011 American Mathematical Society