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In this paper we consider the problem of hedging options in the presence of cost in trading
the underlying asset. This work is an asymptotic analysis of a stochastic control problem,
as in Hodges & Neuberger and Davis, Panas & Zariphopoulou;. We derive a simple
expression for the ‘hedging bandwidth’ around the
Black–Scholes delta; this is the region in
which it is optimal not to rehedge. The effect of the costs on the value of the option, and on
the width of this hedging band is of a significantly greater order of magnitude than the costs
themselves. When costs are proportional to volume traded, rehedging should be done to the
edge of this band; when there are fixed costs present, trading should be done to an optimal
point in the interior of the no-transaction region.
We examine the valuation of American options in a discrete time setting where the exercise price is known a priori but varies with time. (This is in contrast with the classical Black-Scholes  analysis, which lies in a continuous time framework and with constant exercise price.) In particular we consider a time series of exercise prices which are themselves a realisation of the share price random walk — that of the previous year, say.
A simple model is presented for an aerofoil with a recirculating Prandtl-Batchelor region behind a spoiler. Using thin aerofoil theory the model is posed as a pair of coupled nonlinear singular integrodifferential equations for the shape of the separating streamline and the distribution of vorticity along the aerofoil. These equations are solved numerically and results are presented. In particular, some conclusions are drawn regarding the lift on such aerofoils.
We examine the Black–Scholes partial differential equation for the pricing of a traded option (an American call option on an asset paying a continuous dividend) and make comparisons with other well known free boundary diffusion problems, such as the oxygen consumption problem. The pricing of American options can be viewed as a free boundary problem and is, therefore, inherently nonlinear. We consider the short and long time behaviour of the free boundary, present analytic results for the option value in such limits, and consider the formulation of the problem as a variational inequality, and its numerical solution.
We consider the extensional flow and twist of a finite, slender, nearly straight, Newtonian viscous fibre when its ends are drawn apart at prescribed velocity. The initial cross-section of the fibre may be arbitrary and may vary gradually in the axial direction. We derive the leading-order equations for the fibre's free surface and its flow velocity from a regular perturbation expansion of the full Stokes’ flow problem in powers of the aspect ratio. In order to obtain these equations systematically, it is necessary to consider terms beyond the leading order in the perturbation expansion, because those obtainable from the leading-order terms give an indeterminate set of equations. Our results are a pair of well-known hyperbolic equations for the area and axial velocity, together with (i) straightness of the line of centres of mass of the cross-section and (ii) a new hyperbolic evolution equation for the twist of the cross-section. It is only through this hyperbolic equation that history effects are manifest.
We report a non-significantly higher growth hormone (GH) response to intravenous clonidine administration (150 μg) in 10 male patients with panic disorder who had never received antidepressant therapy than in 10 matched controls. These results are consistent with data suggesting a normal or increased adrenergic receptor sensitivity in panic disorder patients.
We consider inviscid, incompressible flow down a backward-facing step. Using thin-aerofoil theory, a model is proposed in which the separated region downstream of the back face of the step consists of a constant-pressure zone immediately behind the step, followed by a Prandtl–Batchelor constant-vorticity region. The motivation for this model is a series of experimental studies which showed the pressure just downstream of the step to be almost constant in some upstream portion of the separated region. Previous models have ignored this constant-pressure region and agreement with experiment has not been good. Agreement with experiment is clearly superior using the constant-pressure/constant-vorticity model, though it is possible that the comparison could be improved still further by consideration of the behaviour of the shear layer after reattachment. Some discussion of such models is given.
Deux patients, un homme de 43 ans et une femme de 24 ans, répondant aux critères diagnostiques du trouble obsessionnel compulsif ont été traités par ocytocine à 10 UI/jour, en intramusculaire. L'ocytocine est un nona-peptide hypophysaire dont la propriété d'altérer la mémoire est connue chez l'animal et chez l'homme. Une rémission relative du trouble obsessionnel compulsif a récemment été signalée lors d'un traitement prolongé par ocytocine intranasale. Nous n'avons, quant à nous, observé aucune amélioration des symptômes obsessionnels compulsifs (évalués selon la liste du Maudsley Hospital) durant les 15 à 20 jours de traitement. Les implications liées au mode d'administration sont discutées, de même que le rôle joué par d'éventuelles manifestations psychopathologiques survenant en cours de traitement.
An unsteady lifting-line theory is presented for a general motion of a wing of high aspect ratio. Our matched-asymptotic-expansions analysis parallels that of Van Dyke (1964) in his solution for the steady lifting line, but is complicated by the shedding of transverse vortices associated with variation of circulation with time. The principal result is an expression for the downwash due to three-dimensional effects. Numerical calculations are presented for a wing of elliptic planform following a curved path.
The classical hydrodynamical problem of a body submerged beneath a free surface is considered. The flow is two-dimensional and the cross-section of the body and its motion are arbitrary. In the limit as a typical body dimension becomes small compared with its depth the method of matched asymptotic expansions becomes applicable and expressions for the forces and moment experienced by the body can be found. Several cases are considered in detail where the body is permitted to move in response to the forces and moment. We also find the additional forces, due to the free surface, experienced by a lifting body - a body about which there is a circulation.
An unsteady lifting line theory for a general motion of a wing of high aspect ratio is presented. Our analysis parallels that of Van Dyke (1964) in his solution for the steady lifting line by the method of matched asymptotic expansions but is complicated by the shedding of transverse vortices associated with variation of circulation with time. We find expressions for the downwash due to three-dimensional (finite span) effects and the lift on the wing. Calculations are presented for a wing of elliptic planform following a curved path.
Heredity has been shown to be an important factor in the aetiology of manic-depressive psychosis. Recent linkage studies with colour blindness have suggested the presence of an X-linked dominant gene in the transmission of manic-depressive psychosis. We report here positive evidence of a linkage between manic-depressive psychosis and glucose-6-phosphate dehydrogenase deficiency in an informative family assorting for both traits. These results strengthen previous linkage studies in affective illness and support the hypothesis of X-linkage in a subgroup of manic-depressive psychosis.
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