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

 

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


Authors: Yu. S. Mishura and Yu. V. Yukhnovs’kiĭ
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 87-101
MSC (2010): Primary 60G44, 60F05, 60B12
Published electronically: August 4, 2011
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Abstract: We study sufficient conditions for the convergence of value processes of self-financial strategies in the case of a $ d$-dimensional financial market with continuous time. The conditions for the weak convergence of value processes are discussed in detail for the Black-Scholes market model. We also consider the ``inverse'' problem for the weak convergence of risk-minimizing strategies.


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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
Email: myus@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/S0094-9000-2011-00829-0
PII: S 0094-9000(2011)00829-0
Keywords: Stochastic integrals, functional limit theorems, weak convergence, semimartingales, semifinancing strategies
Received by editor(s): March 22, 2010
Published electronically: August 4, 2011
Additional Notes: The first author is indebted to the European Commission for support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2011 American Mathematical Society