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October 2015 A model for a large investor trading at market indifference prices. II: Continuous-time case
Peter Bank, Dmitry Kramkov
Ann. Appl. Probab. 25(5): 2708-2742 (October 2015). DOI: 10.1214/14-AAP1059

Abstract

We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the investor’s orders and trade among themselves to attain Pareto optimal allocations. We first consider the case of simple strategies and then, in analogy to the construction of stochastic integrals, investigate the transition to general continuous dynamics. As a result, we show that the model’s evolution can be described by a nonlinear stochastic differential equation for the market makers’ expected utilities.

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Peter Bank. Dmitry Kramkov. "A model for a large investor trading at market indifference prices. II: Continuous-time case." Ann. Appl. Probab. 25 (5) 2708 - 2742, October 2015. https://doi.org/10.1214/14-AAP1059

Information

Received: 1 September 2011; Revised: 1 January 2014; Published: October 2015
First available in Project Euclid: 30 July 2015

zbMATH: 1338.91123
MathSciNet: MR3375887
Digital Object Identifier: 10.1214/14-AAP1059

Subjects:
Primary: 91G10 , 91G20
Secondary: 52A41 , 60G60

Keywords: Bertrand competition , contingent claims , Equilibrium , indifference prices , large investor , liquidity , nonlinear stochastic integral , Pareto allocation , price impact , Random field , saddle functions

Rights: Copyright © 2015 Institute of Mathematical Statistics

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Vol.25 • No. 5 • October 2015
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