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- W2110921408 abstract "We study a constrained stochastic control problem with jumps; the jump times of the controlled process are given by a Poisson process. The cost functional comprises quadratic components for an absolutely continuous control and the controlled process and an absolute value component for the control of the jump size of the process. We characterize the value function by a “polynomial” of degree two whose coefficients depend on the state of the system; these coefficients are given by a coupled system of ODEs. The problem hence reduces from solving the Hamilton Jacobi Bellman (HJB) equation (i.e., a PDE) to solving an ODE whose solution is available in closed form. The state space is separated by a time dependent boundary into a continuation region where the optimal jump size of the controlled process is positive and a stopping region where it is zero. We apply the optimization problem to a problem faced by investors in the financial market who have to liquidate a position in a risky asset and have access to a dark pool with adverse selection." @default.
- W2110921408 created "2016-06-24" @default.
- W2110921408 creator A5039513342 @default.
- W2110921408 date "2014-11-01" @default.
- W2110921408 modified "2023-09-25" @default.
- W2110921408 title "An Explicit Solution of a Nonlinear-Quadratic Constrained Stochastic Control Problem with Jumps: Optimal Liquidation in Dark Pools with Adverse Selection" @default.
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- W2110921408 doi "https://doi.org/10.1287/moor.2014.0649" @default.
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