We study the problem of a trader who wants to maximize the expected revenue from liquidating a given stock position. We model the stock price dynamics as a geometric pure jump process with local characteristics driven by an unobservable finite-state Markov chain and by the liquidation rate. This reflects uncertainty about activity of other traders and feedback effects from trading . We use stochastic filtering to reduce the optimization problem under partial information to an equivalent one under complete information. This leads to a  control problem for piecewise deterministic Markov processes (PDMPs). We apply control theory for PDMPs to our problem. In particular, we derive the optimality equation for the value function, we characterize the value function as  viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with a detailed analysis of a specific example. We present numerical results illustrating the impact of partial information and feedback effects on the value function and on the optimal liquidation rate.
We study the optimal liquidation problem in a market model where the bid price follows a geometric pure jump process whose local characteristics are driven by an unobservable finite-state Markov chain and by the liquidation rate. This model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis . We use stochastic filtering to reduce the optimal liquidation problem to an equivalent optimization problem under complete information. This leads to a stochastic control problem for piecewise deterministic Markov processes (PDMPs). We carry out a detailed mathematical analysis of this problem. In particular, we derive the optimality equation for the value function, we characterize the value function as continuous viscosity solution of the associated dynamic programming equation, and we prove a novel comparison result. The paper concludes with numerical results illustrating the impact of partial information and price impact on the value function and on the optimal liquidation rate.
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problem of a trader who wants to maximize the expected revenue from liquidating a given stock position. We model the stock price dynamics as
optimal liquidation problem in a market model where the bid price follows
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with local characteristics
whose local characteristics are
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reflects uncertainty about activity of other traders and feedback effects from trading
model is consistent with stylized facts of high frequency data such as the discrete nature of tick data and the clustering in the order flow. We include both temporary and permanent effects into our analysis
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optimization problem under partial information
optimal liquidation problem
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one
optimization problem
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stochastic
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apply control theory for PDMPs to our
carry out a detailed mathematical analysis of this
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continuous
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a detailed analysis of a specific example. We present
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feedback effects
price impact