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.
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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.
- Dana, R. A. & Le Van, C., 1996. "Asset Equilibria in Lp spaces with complete markets: A duality approach," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 263-280.
- 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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