Geodesic
The stochastic field of aggregate utilities and its saddle conjugate
Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 21-60

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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. 
@article{TRSPY_2014_287_a2,
     author = {P. Bank and D. Kramkov},
     title = {The stochastic field of aggregate utilities and its saddle conjugate},
     journal = {Informatics and Automation},
     pages = {21--60},
     publisher = {mathdoc},
     volume = {287},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a2/}
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P. Bank; D. Kramkov. The stochastic field of aggregate utilities and its saddle conjugate. Informatics and Automation, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 21-60. http://geodesic.mathdoc.fr/item/TRSPY_2014_287_a2/