LRA Collection:
http://hdl.handle.net/2381/4819
20140419T02:26:23Z

Polynomial programming approach to weak approximation of Lévydriven stochastic differential equations with application to option pricing
http://hdl.handle.net/2381/10216
Title: Polynomial programming approach to weak approximation of Lévydriven stochastic differential equations with application to option pricing
Authors: Kashima, Kenji; Kawai, Reiichiro
Abstract: We propose an optimization approach to weak approximation of Levydriven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Levy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We present numerical examples of the computation of the moments, as well as the European call option premium, of the DoleacuteansDade exponential model.
20120319T16:46:22Z

An optimization approach to weak approximation of Lévydriven stochastic differential equations with application to option pricing
http://hdl.handle.net/2381/10189
Title: An optimization approach to weak approximation of Lévydriven stochastic differential equations with application to option pricing
Authors: Kashima, Kenji; Kawai, Reiichiro
Abstract: We propose an optimization approach to weak
approximation of Lévydriven stochastic differential equations.
We employ a mathematical programming framework to obtain
numerically upper and lower bound estimates of the target
expectation, where the optimization procedure ends up with
a polynomial programming problem. An advantage of our
approach is that all we need is a closed form of the Lévy
measure, not the exact simulation knowledge of the increments
or of a shot noise representation for the time discretization
approximation. We also investigate methods for approximation
at some different intermediate time points simultaneously.
Description: Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
20120314T11:34:46Z

Transition mechanisms within the boundarylayer flow over slender vs. broad rotating cones
http://hdl.handle.net/2381/8867
Title: Transition mechanisms within the boundarylayer flow over slender vs. broad rotating cones
Authors: Hussain, Z.; Garrett, Stephen J.; Stephen, S.O.
Abstract: We describe progress in classifying the convective instability characteristics of the boundarylayer
flow over the family of rotating cones. Existing experimental and theoretical studies
are discussed which lead to the clear hypothesis of a centrifugal instability mode that dominates
over slender cones and manifests as Görtlertype spiral vortices. Although a formulation
consistent with the classic rotatingdisk problem has been successful in predicting the
stability characteristics over broad cones, it is unable to identify such a centrifugal mode
as the halfangle is reduced. An alternative formulation is introduced and an asymptotic
analysis summarized which identifies such a centrifugal mode.
Description: This paper was published as Proceedings of the 40th Fluid Dynamics Conference and Exhibit, 28 June  1 July 2010, Chicago, Illinois, Paper AIAA20104285. It is also available from http://www.aiaa.org/content.cfm?pageid=2. This paper appears here with the permission of the American Institute of Aeronautics and Astronautics, Inc.
20101213T15:20:13Z

The convective instability of boundarylayer flows over rotating spheroids
http://hdl.handle.net/2381/8849
Title: The convective instability of boundarylayer flows over rotating spheroids
Authors: Samad, A.; Garrett, S.J.
Abstract: The continuous development of spinning projectiles and
other industrial applications has led to the need to understand the
laminar boundarylayer flow and subsequent onset of transition
over the general family of rotating spheroids.
We begin by finding the laminar boundarylayer flow over a
general spheroid. In particular, we distinguish between prolate
and oblate spheroids and use an appropriate spheroidal coordinate
system in each case. The laminarflow equations are established
for each family of spheroid rotating in otherwise still
fluid. An eccentricity parameter e is used to distinguish particular
bodies within the oblate or prolate families. In each case,
setting e = 0 reduces the equations to those already established
by Howarth [2] and Banks [4] for the rotating sphere.
In this preliminary study the laminarflow equations at each
latitude are solved by extending the original series solutions due
to Howarth and Banks for the rotating sphere. The laminar flows
obtained are consistent with established results for the rotating
sphere as e tends to zero, and tend to the von Kármán [5] solution
for the rotating disk as the latitude is reduced close to the nose.
Analyses of the convective instability are performed on the
rotating prolate family. These extend the linear analyses previously
published by Malik, Lingwood and Garrett & Peake [6–10]
on related geometries. An investigation into the relative importance
of type I (crossflow) and type II (streamline curvature)
modes is also presented. At low latitudes increasing eccentricity
has negligible effects on the stability characteristics of the flow. However as the latitude increases, eccentricity is seen to
lower the upper (type I) branch of the neutral curve, reducing the
region of instability.
Description: This paper was published in Proceedings of FEDSM2009, ASME 2009 Fluids Engineering Summer Meeting, August 25, 2009, Vail, Colorado USA. It is available from http://www.asme.org/Publications/ConfProceedings/. Doi: 10.1115/FEDSM200978484; Metadata only entry
20101208T15:48:56Z

On the global linear stability of the boundary layer on rotating bodies
http://hdl.handle.net/2381/8847
Title: On the global linear stability of the boundary layer on rotating bodies
Authors: Garrett, S.J.; Peake, N.
Abstract: By taking the local approach of working at a fixed Reynolds number (equivalently
at fixed distance from the axis of rotation) and assuming that the
steady flow is spatially uniform, [1] shows that the boundary layer on a rotating
disk is locally absolutely unstable at Reynolds numbers in excess of a
critical value. The value of the critical Reynolds number agrees exceedingly
well with experimentally measured values of the transition Reynolds number,
leading to a clear hypothesis that absolute instability plays a role in turbulent
transition on the disk.
In contrast to this local analysis, [2] solve the linearised Navier–Stokes
equations directly for the rotating disk. When they make the same homogenous
flow approximation as in [1], they recover those results in full. However,
when the spatial inhomogeneity of the boundary layer is included there is no
evidence of an unstable global oscillator in the longterm response.
In order to address this discrepancy between the local results and the
numerical simulations of the full inhomogeneous flow, we consider the linear
global modes of the rotating disk/cone boundary layer.
Description: This paper was published as Advances in Turbulence XI: Proceedings of the 11th EUROMECH European Turbulence Conference, June 2528, 2007, Porto, Portugal; Palma, J. M. L. M.; Silva Lopes, A. (Eds.), pp. 550552. It is available from http://www.springer.com/materials/mechanics/book/9783540726036; Metadata only entry
20101208T15:23:09Z

Boundarylayer transition on broad cones rotating in an imposed axial flow
http://hdl.handle.net/2381/8838
Title: Boundarylayer transition on broad cones rotating in an imposed axial flow
Authors: Garrett, Stephen J.; Hussain, Z.; Stephen, S.O.
Abstract: We present stability analyses for the boundarylayer flow over broad cones (halfangle
> 40◦) rotating in imposed axial flows. Preliminary convective instability analyses are
presented that are based on the Orr–Sommerfeld equation for a variety of axialflow speeds.
The results are discussed in terms of the limited existing experimental data and previous
stability analyses on related bodies. The results of an absolute instability analysis are also
presented which are intended to further those by Garrett & Peake through the use of
a more rigorous steadyflow formulation. Axial flow is seen to delay the onset of both
convective and absolute instabilities.
Description: This paper was originally presented at and published in the Proceedings of the 39th AIAA Fluid Dynamics Conference, San Antonio, Texas, June 2225, 2009. It was subsequently published as AIAA Journal, 48 (6), pp. 11841194. This paper is reprinted with the permission of the American Institute of Aeronautics and Astronautics, Inc. It is also available from http://www.aiaa.org/content.cfm?pageid=2. Doi: 10.2514/1.50233
20101207T14:22:52Z

A Selective Review of Transition Modelling for CFD.
http://hdl.handle.net/2381/7645
Title: A Selective Review of Transition Modelling for CFD.
Authors: Di Pasquale, Davide; Rona, Aldo; Garrett, Stephen J.
Abstract: This paper aims to give an overview of the more widely used approaches to model transition
in Computational Fluid Dynamics (CFD). Eight different methods are reviewed: the
stability theory approach, the low Reynolds number turbulent closure approach, the intermittency
transport method with integral correlations, the intermittency and the vorticity
Reynolds number approach, the laminar fluctuation energy method, the ν/2 f model, and
the Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for transition.
The approaches are compared to one another, highlighting their respective advantages and
drawbacks. From this analysis, a list of desirable features for CFD transition models is
drawn up, against which the eight approaches are scored.
Description: This paper was presented at the 39th AIAA Fluid Dynamics Conference, San Antonio, Texas, June 2225, 2009. Copyright © 2009 by the American Institute of Aeronautics and Astronautics. It is available from http://www.aiaa.org/content.cfm?pageid=406. It appears here with the permission of the American Institute of Aeronautics and Astronautics Inc.
20100308T14:21:38Z

Moduli stacks of vector bundles and Frobenius morphisms
http://hdl.handle.net/2381/3451
Title: Moduli stacks of vector bundles and Frobenius morphisms
Authors: Neumann, Frank; Stuhler, Ulrich
20091208T16:13:12Z

Nonuniform smallgain theorems for systems with unstable invariant sets
http://hdl.handle.net/2381/4820
Title: Nonuniform smallgain theorems for systems with unstable invariant sets
Authors: Tyukin, Ivan Yu.; Steur, Erik; Nijmeijer, Henk; van Leeuwen, Cees
Abstract: We consider the problem of smallgain analysis of asymptotic behavior in interconnected nonlinear dynamic systems. Mathematical models of these systems are allowed to be uncertain and timevarying. In contrast to standard smallgain theorems that require global asymptotic stability of each interacting component in the absence of inputs, we consider interconnections of systems that can be critically stable and have infinite inputoutput Linfin gains. For this class of systems we derive smallgain conditions specifying state boundedness of the interconnection. The estimates of the domain in which the systempsilas state remains are also provided. Conditions that follow from the main results of our paper are nonuniform in space. That is they hold generally only for a set of initial conditions in the systempsilas state space. We show that under some mild continuity restrictions this set has a nonzero volume, hence such bounded yet potentially globally unstable motions are realizable with a nonzero probability. Proposed results can be used for the design and analysis of intermittent, itinerant and metastable dynamics which is the case in the domains of control of chemical kinetics, biological and complex physical systems, and nonlinear optimization.
Description: This is the author's final draft of the paper published as Decision and Control, 2008, CDC 2008, 47th IEEE Conference on, Proceedings of, pp. 5080  5085. Copyright © 2008 IEEE. Doi: 10.1109/CDC.2008.4739503. This material is posted here with permission of the IEEE. Such permission
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20091201T14:44:31Z