Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Trade Execution Under Endogenous Pressure to Liquidate: Theory
  and Numerical Solutions   We study optimal liquidation of a trading position (so-called block order or
meta-order) in a market with a linear temporary price impact (Kyle, 1985). We
endogenize the pressure to liquidate by introducing a downward drift in the
unaffected asset price while simultaneously ruling out short sales. In this
setting the liquidation time horizon becomes a stopping time determined
endogenously, as part of the optimal strategy. We find that the optimal
liquidation strategy is consistent with the square-root law which states that
the average price impact per share is proportional to the square root of the
size of the meta-order (Bershova and Rakhlin, 2013; Farmer et al., 2013; Donier
et al., 2015; T\'oth et al., 2016).
  Mathematically, the Hamilton-Jacobi-Bellman equation of our optimization
leads to a severely singular and numerically unstable ordinary differential
equation initial value problem. We provide careful analysis of related singular
mixed boundary value problems and devise a numerically stable computation
strategy by re-introducing time dimension into an otherwise time-homogeneous
task.

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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: econ