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

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.

Published at http://dx.doi.org/10.1214/14-AAP1059 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

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

Cited by in corpus (8)

• Markovian Nash equilibrium in financial markets with asymmetric information and related forward-backward systems
• Hedging, arbitrage and optimality with superlinear frictions
• A model for a large investor trading at market indifference prices. I: single-period case
• Integral representation of martingales motivated by the problem of endogenous completeness in financial economics
• On a stochastic differential equation arising in a price impact model
• The stochastic field of aggregate utilities and its saddle conjugate
• Perfect hedging under endogenous permanent market impacts
• Efficient price dynamics in a limit order market: an utility indifference approach