We establish existence and uniqueness of a classical solution to a semilinear parabolic partial differential equation with singular initial condition. This equation describes the value function of the control problem of a financial 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.
We consider the stochastic control problem of a financial 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 prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior at the terminal time , and give the optimal trading strategy in feedback form.
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establish existence and uniqueness of a classical solution to a semilinear parabolic partial differential equation with singular initial condition. This equation describes the value function of the
consider the stochastic
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price dependent
price-dependent
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price dependent
price-dependent
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establish the explicit asymptotic behavior of the value function
prove that the value function can be characterized in terms of the unique smooth solution to a PDE with singular terminal value, establish its explicit asymptotic behavior
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