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Teoriya Veroyatnostei i ee Primeneniya, 2024, Volume 69, Issue 4, Pages 653–667
DOI: https://doi.org/10.4213/tvp5740 (Mi tvp5740) 		 
Martingale methods in problems of existence of survival strategies

M. V. Zhitlukhin, A. A. Tokaeva

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5740
Abstract: We consider a model of a financial market with endogenous asset prices. An agent's strategy is called survival if its share of the total market wealth is bounded away from zero over the infinite time horizon regardless of the strategies used by the other agents. We obtain necessary and sufficient conditions for survival of strategies, which generalize known results that deal with construction of such strategies or only with necessary conditions for survival. The proofs rely mainly on martingale convergence theorems.
Keywords: mathematical finance, endogenous prices, survival strategies, martingale convergence.
Funding agency Grant number
Russian Science Foundation 24-71-10109
Received: 15.08.2024
Accepted: 15.08.2024
English version:
Theory of Probability and its Applications, 2025, Volume 69, Issue 4, Pages 520–530
DOI: https://doi.org/10.1137/S0040585X97T992100
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Zhitlukhin, A. A. Tokaeva, “Martingale methods in problems of existence of survival strategies”, Teor. Veroyatnost. i Primenen., 69:4 (2024), 653–667; Theory Probab. Appl., 69:4 (2025), 520–530
Citation in format AMSBIB
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\by M.~V.~Zhitlukhin, A.~A.~Tokaeva
\paper Martingale methods in problems of existence of survival strategies
\jour Teor. Veroyatnost. i Primenen.
\yr 2024
\vol 69
\issue 4
\pages 653--667
\mathnet{http://mi.mathnet.ru/tvp5740}
\crossref{https://doi.org/10.4213/tvp5740}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 69
\issue 4
\pages 520--530
\crossref{https://doi.org/10.1137/S0040585X97T992100}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-86000037857}
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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