Geodesic
The stochastic field of aggregate utilities and its saddle conjugate
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
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P. Bank; D. Kramkov. The stochastic field of aggregate utilities and its saddle conjugate. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 21-60. http://geodesic.mathdoc.fr/item/TM_2014_287_a2/

[1] Bank P., Kramkov D., A model for a large investor trading at market indifference prices. I: Single-period case, E-print, 2011, arXiv: 1110.3224v2 [q-fin.TR]

[2] Bank P., Kramkov D., A model for a large investor trading at market indifference prices. II: Continuous-time case, E-print, 2011., arXiv: 1110.3229v2 [q-fin.TR]

[3] Bank P., Kramkov D., “On a stochastic differential equation arising in a price impact model”, Stoch. Processes Appl., 123:3 (2013), 1160–1175 | DOI | MR | Zbl

[4] Dana R.-A., “Existence, uniqueness and determinacy of Arrow–Debreu equilibria in finance models”, J. Math. Econ., 22:6 (1993), 563–579 | DOI | MR | Zbl

[5] Dana R.A., Le Van C., “Asset equilibria in $L^p$ spaces with complete markets: A duality approach”, J. Math. Econ., 25:3 (1996), 263–280 | DOI | MR | Zbl

[6] Hiriart-Urruty J.-B., Lemaréchal C., Fundamentals of convex analysis, Grundl. Text Ed., Springer, Berlin, 2001 | MR | Zbl

[7] Karatzas I., Lehoczky J.P., Shreve S.E., “Existence and uniqueness of multi-agent equilibrium in a stochastic, dynamic consumption/investment model”, Math. Oper. Res., 15:1 (1990), 80–128 | DOI | MR | Zbl

[8] Kunita H., Stochastic flows and stochastic differential equations, Cambridge Stud. Adv. Math., 24, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl

[9] Milgrom P., Segal I., “Envelope theorems for arbitrary choice sets”, Econometrica, 70:2 (2002), 583–601 | DOI | MR | Zbl

[10] Rockafellar R.T., Convex analysis, Princeton Math. Ser., 28, Princeton Univ. Press, Princeton, NJ, 1970 | MR

[11] Rockafellar R.T., Wets R.J.-B., Variational analysis, Grundl. Math. Wiss., 317, Springer, Berlin, 1998 | MR | Zbl