Stability for gains from large investors' strategies in M1/J1 topologies

Dirk Becherer, Todor Bilarev and Peter Frentrup

Papers from arXiv.org

Abstract: We prove continuity of a controlled SDE solution in Skorokhod's $M_1$ and $J_1$ topologies and also uniformly, in probability, as a non-linear functional of the control strategy. The functional comes from a finance problem to model price impact of a large investor in an illiquid market. We show that $M_1$-continuity is the key to ensure that proceeds and wealth processes from (self-financing) c\`{a}dl\`{a}g trading strategies are determined as the continuous extensions for those from continuous strategies. We demonstrate by examples how continuity properties are useful to solve different stochastic control problems on optimal liquidation and to identify asymptotically realizable proceeds.

Date: 2017-01, Revised 2018-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Bernoulli, Volume 25, Number 2 (2019), 1105-1140

Downloads: (external link)
http://arxiv.org/pdf/1701.02167 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1701.02167

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().