The Annals of Applied Probability

A model for a large investor trading at market indifference prices. II: Continuous-time case

Peter Bank and Dmitry Kramkov

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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.

Article information

Ann. Appl. Probab., Volume 25, Number 5 (2015), 2708-2742.

Received: September 2011
Revised: January 2014
First available in Project Euclid: 30 July 2015

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Zentralblatt MATH identifier

Primary: 91G10: Portfolio theory 91G20: Derivative securities
Secondary: 52A41: Convex functions and convex programs [See also 26B25, 90C25] 60G60: Random fields

Bertrand competition contingent claims equilibrium indifference prices liquidity large investor Pareto allocation price impact saddle functions nonlinear stochastic integral random field


Bank, Peter; Kramkov, Dmitry. A model for a large investor trading at market indifference prices. II: Continuous-time case. Ann. Appl. Probab. 25 (2015), no. 5, 2708--2742. doi:10.1214/14-AAP1059.

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