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December 2017 Financial markets with a large trader
Tilmann Blümmel, Thorsten Rheinländer
Ann. Appl. Probab. 27(6): 3735-3786 (December 2017). DOI: 10.1214/17-AAP1295


We construct a large trader model using tools from nonlinear stochastic integration theory and an impact function. It encompasses many well-known models from the literature. In particular, the model allows price changes to depend on the size as well as on the speed and timing of the large trader’s transactions. Moreover, a volume impact limit order book can be studied in this framework. Relaxing a condition about existence of a universal martingale measure governing all resulting small trader models, we can show absence of arbitrage for the small trader under mild conditions. Furthermore, a case study on utility maximization from terminal wealth highlights new phenomena that can arise in our framework. Finally, an outlook on further research provides insights on (no) arbitrage opportunities for the large trader and how different levels of information may affect our analysis.


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Tilmann Blümmel. Thorsten Rheinländer. "Financial markets with a large trader." Ann. Appl. Probab. 27 (6) 3735 - 3786, December 2017.


Received: 1 December 2015; Revised: 1 November 2016; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06848278
MathSciNet: MR3737937
Digital Object Identifier: 10.1214/17-AAP1295

Primary: 60H05 , 91G10

Keywords: Large trader , limit order book , no arbitrage , nonlinear stochastic integration , Portfolio optimization

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 6 • December 2017
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