65 research outputs found
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A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
We consider the ordinary differential equation
x2u′′=axu′+bu−c(u′−1)2,x∈(0,x0),
with
a∈R,b∈R
, c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x 0=∞ which is such that 0≤u(x)≤x for all x>0, and that this solution is strictly increasing and concave
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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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Erratum to: A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics
Erratum to: Appl Math Optim (2013) 68:255–274 DOI 10.1007/s00245-013-9205-
A cryogenic axial-centrifugal compressor for superfluid helium refrigeration
CERN's new project, the Large Hadron Collider (LHC), will use superfluid helium as coolant for its high-field superconducting magnets and therefore require large capacity refrigeration at 1.8 K. This may only be achieved by subatmospheric compression of gaseous helium at cryogenic temperature. To stimulate development of this technology, CERN has procured from industry prototype Cold Compressor Units (CCU). This unit is based on a cryogenic axial-centrifugal compressor, running on ceramic ball bearings and driven by a variable-frequency electrical motor operating under low-pressure helium at ambient temperature. The machine has been commissioned and is now in operation. After describing basic constructional features of the compressor, we report on measured performance
Operational Experience with a Cryogenic Axial-Centrifugal Compressor
The Large Hadron Collider (LHC), presently under construction at CERN, requires large refrigeration capacity at 1.8 K. Compression of gaseous helium at cryogenic temperatures is therefore inevitable. Together with subcontractors, Linde Kryotechnik has developed a prototype machine. This unit is based on a cryogenic axial-centrifugal compressor, running on ceramic ball bearings and driven by a variable-frequency electrical motor operating at ambient temperature. Integrated in a test facility for superconducting magnets the machine has been commissioned without major problems and successfully gone through the acceptance test in autumn 1995. Subsequent steps were initiated to improve efficiency of this prototype. This paper describes operating experience gained so far and reports on measured performance prior to and after constructional modifications
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
Controllability on infinite-dimensional manifolds
Following the unified approach of A. Kriegl and P.W. Michor (1997) for a
treatment of global analysis on a class of locally convex spaces known as
convenient, we give a generalization of Rashevsky-Chow's theorem for control
systems in regular connected manifolds modelled on convenient
(infinite-dimensional) locally convex spaces which are not necessarily
normable.Comment: 19 pages, 1 figur
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