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Smooth solutions to portfolio liquidation problems under price-sensitive market impact

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Co-authors: Paulwin Graewe, Eric Sere

We establish existence and uniqueness of a classical solution to a semilinear parabolic partial dierential equation with singular initial condition. This equation describes the value function of the control problem of a nancial trader that needs to unwind a large asset portfolio within a short period of time. The trader can simultaneously submit active orders to a primary market and passive orders to a dark pool. Our framework is flexible enough to allow for price dependent impact functions describing the trading costs in the primary market and price dependent adverse selection costs associated with dark pool trading. We establish the explicit asymptotic behavior of the value function at the terminal time and give the optimal trading strategy in feedback form.

This talk is part of the Isaac Newton Institute Seminar Series series.

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