Functional limit theorems for stochastic integrals with applications to risk processes and to selffinancing 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), 131146
MSC (2010):
Primary 60G44, 60F05, 60B12
Published electronically:
January 20, 2011
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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:
http://dx.doi.org/10.1090/S009490002011008150
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 PIRSESGA2008230804
Article copyright:
© Copyright 2011
American Mathematical Society
