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

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  • Dirk Becherer
  • Todor Bilarev
  • Peter Frentrup

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.

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  • Dirk Becherer & Todor Bilarev & Peter Frentrup, 2017. "Stability for gains from large investors' strategies in M1/J1 topologies," Papers 1701.02167, arXiv.org, revised Mar 2018.
    • Handle: RePEc:arx:papers:1701.02167
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    References listed on IDEAS

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    Cited by:

    1. Ferrari, Giorgio & Koch, Torben, 2018. "An optimal extraction problem with price impact," Center for Mathematical Economics Working Papers 603, Center for Mathematical Economics, Bielefeld University.
    2. Giorgio Ferrari & Torben Koch, 2018. "An Optimal Extraction Problem with Price Impact," Papers 1812.01270, arXiv.org.

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