The stochastic field of aggregate utilities and its saddle conjugate
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.
|Date of creation:||Oct 2013|
|Date of revision:|
|Publication status:||Published in Tr. Mat. Inst. Steklova, 2014, Volume 287, Pages 21-60|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Dana, R.A. & Le Van, C., 1996.
"Asset Equilibria in "L" Spaces with Complete Markets: A Duality Approach,"
95.388, Toulouse - GREMAQ.
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- Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
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