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

Full-text: Open access

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1438261052

Digital Object Identifier
doi:10.1214/14-AAP1059

Mathematical Reviews number (MathSciNet)
MR3375887

Zentralblatt MATH identifier
1338.91123

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

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

Citation

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. https://projecteuclid.org/euclid.aoap/1438261052


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