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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 287, Pages 21–60
DOI: https://doi.org/10.1134/S0371968514040037 (Mi tm3581) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The stochastic field of aggregate utilities and its saddle conjugate

P. Banka, D. Kramkovbc

a Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
b University of Oxford, Oxford, UK
c Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA, USA
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DOI: https://doi.org/10.1134/S0371968514040037
Abstract: We describe the sample paths of the stochastic field $F=F_t(v,x,q)$ of aggregate utilities parameterized by Pareto weights $v$ and total cash amounts $x$ and stocks' quantities $q$ in an economy. We also describe the sample paths of the stochastic field $G=G_t(u,y,q)$, which is conjugate to $F$ with respect to the saddle arguments $(v,x)$, and obtain various conjugacy relations between these stochastic fields. The results of this paper play a key role in our study of a continuous-time price impact model.
Received in January 2014
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 287, Issue 1, Pages 14–53
DOI: https://doi.org/10.1134/S0081543814080033
Bibliographic databases:
Document Type: Article
UDC: 519.86
Language: English
Citation: P. Bank, D. Kramkov, “The stochastic field of aggregate utilities and its saddle conjugate”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 21–60; Proc. Steklov Inst. Math., 287:1 (2014), 14–53
Citation in format AMSBIB
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\by P.~Bank, D.~Kramkov
\paper The stochastic field of aggregate utilities and its saddle conjugate
\inbook Stochastic calculus, martingales, and their applications
\bookinfo Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 287
\pages 21--60
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968514040037}
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    • This publication is cited in the following 3 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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