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The stochastic field of aggregate utilities and its saddle conjugate

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  • Peter Bank
  • Dmitry Kramkov

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.

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  • Peter Bank & Dmitry Kramkov, 2013. "The stochastic field of aggregate utilities and its saddle conjugate," Papers 1310.7280, arXiv.org.
    • Handle: RePEc:arx:papers:1310.7280
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    References listed on IDEAS

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    1. 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.
    2. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    3. Ioannis Karatzas & John P. Lehoczky & Steven E. Shreve, 1990. "Existence and Uniqueness of Multi-Agent Equilibrium in a Stochastic, Dynamic Consumption/Investment Model," Mathematics of Operations Research, INFORMS, vol. 15(1), pages 80-128, February.
    4. Bank, Peter & Kramkov, Dmitry, 2013. "On a stochastic differential equation arising in a price impact model," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 1160-1175.
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    Cited by:

    1. Peter Bank & Dmitry Kramkov, 2011. "A model for a large investor trading at market indifference prices. II: Continuous-time case," Papers 1110.3229, arXiv.org, revised Sep 2015.

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