7,282 research outputs found
Optimal Execution with Dynamic Order Flow Imbalance
We examine optimal execution models that take into account both market
microstructure impact and informational costs. Informational footprint is
related to order flow and is represented by the trader's influence on the flow
imbalance process, while microstructure influence is captured by instantaneous
price impact. We propose a continuous-time stochastic control problem that
balances between these two costs. Incorporating order flow imbalance leads to
the consideration of the current market state and specifically whether one's
orders lean with or against the prevailing order flow, key components often
ignored by execution models in the literature. In particular, to react to
changing order flow, we endogenize the trading horizon . After developing
the general indefinite-horizon formulation, we investigate several tractable
approximations that sequentially optimize over price impact and over . These
approximations, especially a dynamic version based on receding horizon control,
are shown to be very accurate and connect to the prevailing Almgren-Chriss
framework. We also discuss features of empirical order flow and links between
our model and "Optimal Execution Horizon" by Easley et al (Mathematical
Finance, 2013).Comment: 31 pages, 8 figure
Exact and asymptotic solutions of the call auction problem
The call auction is a widely used trading mechanism, especially during the
opening and closing periods of financial markets. In this paper, we study a
standard call auction problem where orders are submitted according to Poisson
processes, with random prices distributed according to a general distribution,
and may be cancelled at any time. We compute the analytical expressions of the
distributions of the traded volume, of the lower and upper bounds of the
clearing prices, and of the price range of these possible clearing prices of
the call auction. Using results from the theory of order statistics and a
theorem on the limit of sequences of random variables with independent random
indices, we derive the weak limits of all these distributions. In this setting,
traded volume and bounds of the clearing prices are found to be asymptotically
normal, while the clearing price range is asymptotically exponential. All the
parameters of these distributions are explicitly derived as functions of the
parameters of the incoming orders' flows.Comment: 24 pages, 7 figure
Quantum phases of atomic Fermi gases with anisotropic spin-orbit coupling
We consider a general anisotropic spin-orbit coupling (SOC) and analyze the
phase diagrams of both balanced and imbalanced Fermi gases for the entire
BCS--Bose-Einstein condensate (BEC) evolution. In the first part, we use the
self-consistent mean-field theory at zero temperature, and show that the
topological structure of the ground-state phase diagrams is quite robust
against the effects of anisotropy. In the second part, we go beyond the
mean-field description, and investigate the effects of Gaussian fluctuations
near the critical temperature. This allows us to derive the time-dependent
Ginzburg-Landau theory, from which we extract the effective mass of the Cooper
pairs and their critical condensation temperature in the molecular BEC limit.Comment: 10 pages with 7 figures; to appear in PR
Parameterized Directed -Chinese Postman Problem and Arc-Disjoint Cycles Problem on Euler Digraphs
In the Directed -Chinese Postman Problem (-DCPP), we are given a
connected weighted digraph and asked to find non-empty closed directed
walks covering all arcs of such that the total weight of the walks is
minimum. Gutin, Muciaccia and Yeo (Theor. Comput. Sci. 513 (2013) 124--128)
asked for the parameterized complexity of -DCPP when is the parameter.
We prove that the -DCPP is fixed-parameter tractable.
We also consider a related problem of finding arc-disjoint directed
cycles in an Euler digraph, parameterized by . Slivkins (ESA 2003) showed
that this problem is W[1]-hard for general digraphs. Generalizing another
result by Slivkins, we prove that the problem is fixed-parameter tractable for
Euler digraphs. The corresponding problem on vertex-disjoint cycles in Euler
digraphs remains W[1]-hard even for Euler digraphs
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