The stochastic field of aggregate utilities and its saddle conjugate

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.

62 pages. arXiv admin note: substantial text overlap with arXiv:1110.3224, arXiv:1110.3229

References in corpus (2)

• A model for a large investor trading at market indifference prices. II: Continuous-time case
• On a stochastic differential equation arising in a price impact model