791 research outputs found
An Optimal Execution Problem with Market Impact
We study an optimal execution problem in a continuous-time market model that
considers market impact. We formulate the problem as a stochastic control
problem and investigate properties of the corresponding value function. We find
that right-continuity at the time origin is associated with the strength of
market impact for large sales, otherwise the value function is continuous.
Moreover, we show the semi-group property (Bellman principle) and characterise
the value function as a viscosity solution of the corresponding
Hamilton-Jacobi-Bellman equation. We introduce some examples where the forms of
the optimal strategies change completely, depending on the amount of the
trader's security holdings and where optimal strategies in the Black-Scholes
type market with nonlinear market impact are not block liquidation but gradual
liquidation, even when the trader is risk-neutral.Comment: 36 pages, 8 figures, a modified version of the article "An optimal
execution problem with market impact" in Finance and Stochastics (2014
Explicitly symmetrical treatment of three-body phase space
We derive expressions for three-body phase space that are explicitly
symmetrical in the masses of the three particles. We study geometrical
properties of the variables involved in elliptic integrals and demonstrate that
it is convenient to use the Jacobian zeta function to express the results in
four and six dimensions.Comment: 20 pages, latex, 2 postscript figure
Calibration of optimal execution of financial transactions in the presence of transient market impact
Trading large volumes of a financial asset in order driven markets requires
the use of algorithmic execution dividing the volume in many transactions in
order to minimize costs due to market impact. A proper design of an optimal
execution strategy strongly depends on a careful modeling of market impact,
i.e. how the price reacts to trades. In this paper we consider a recently
introduced market impact model (Bouchaud et al., 2004), which has the property
of describing both the volume and the temporal dependence of price change due
to trading. We show how this model can be used to describe price impact also in
aggregated trade time or in real time. We then solve analytically and calibrate
with real data the optimal execution problem both for risk neutral and for risk
averse investors and we derive an efficient frontier of optimal execution. When
we include spread costs the problem must be solved numerically and we show that
the introduction of such costs regularizes the solution.Comment: 31 pages, 8 figure
Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact
This paper is a continuation of Ishitani and Kato (2015), in which we derived
a continuous-time value function corresponding to an optimal execution problem
with uncertain market impact as the limit of a discrete-time value function.
Here, we investigate some properties of the derived value function. In
particular, we show that the function is continuous and has the semigroup
property, which is strongly related to the Hamilton-Jacobi-Bellman
quasi-variational inequality. Moreover, we show that noise in market impact
causes risk-neutral assessment to underestimate the impact cost. We also study
typical examples under a log-linear/quadratic market impact function with
Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648
A New MHD Code with Adaptive Mesh Refinement and Parallelization for Astrophysics
A new code, named MAP, is written in Fortran language for
magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR)
and Message Passing Interface (MPI) parallelization. There are several optional
numerical schemes for computing the MHD part, namely, modified Mac Cormack
Scheme (MMC), Lax-Friedrichs scheme (LF) and weighted essentially
non-oscillatory (WENO) scheme. All of them are second order, two-step,
component-wise schemes for hyperbolic conservative equations. The total
variation diminishing (TVD) limiters and approximate Riemann solvers are also
equipped. A high resolution can be achieved by the hierarchical
block-structured AMR mesh. We use the extended generalized Lagrange multiplier
(EGLM) MHD equations to reduce the non-divergence free error produced by the
scheme in the magnetic induction equation. The numerical algorithms for the
non-ideal terms, e.g., the resistivity and the thermal conduction, are also
equipped in the MAP code. The details of the AMR and MPI algorithms are
described in the paper.Comment: 44 pages, 16 figure
Phase-Field Formulation for Quantitative Modeling of Alloy Solidification
A phase-field formulation is introduced to simulate quantitatively
microstructural pattern formation in alloys. The thin-interface limit of this
formulation yields a much less stringent restriction on the choice of interface
thickness than previous formulations and permits to eliminate non-equilibrium
effects at the interface. Dendrite growth simulations with vanishing solid
diffusivity show that both the interface evolution and the solute profile in
the solid are well resolved
Tightness for a stochastic Allen--Cahn equation
We study an Allen-Cahn equation perturbed by a multiplicative stochastic
noise which is white in time and correlated in space. Formally this equation
approximates a stochastically forced mean curvature flow. We derive uniform
energy bounds and prove tightness of of solutions in the sharp interface limit,
and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential
Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new.
It replaces and simplifies the old propositions 6.4-6.
Regularity of higher codimension area minimizing integral currents
This lecture notes are an expanded version of the course given at the
ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa,
September 30th - October 30th 2013. The lectures aim to explain the main steps
of a new proof of the partial regularity of area minimizing integer rectifiable
currents in higher codimension, due originally to F. Almgren, which is
contained in a series of papers in collaboration with C. De Lellis (University
of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real
Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L.
Ambrosio Ed., Edizioni SNS (CRM Series
Multidimensional Phase Space and Sunset Diagrams
We derive expressions for the phase-space of a particle of momentum
decaying into particles, that are valid for any number of dimensions. These
are the imaginary parts of so-called `sunset' diagrams, which we also obtain.
The results are given as a series of hypergeometric functions, which terminate
for odd dimensions and are also well-suited for deriving the threshold
behaviour.Comment: 12 pages, RevTex. 2 minor algebraic corrections to page 4 after eqns
(6) and (8
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