Author

# Sam Howison

Bio: Sam Howison is an academic researcher. The author has contributed to research in topics: Engineering mathematics. The author has an hindex of 1, co-authored 1 publications receiving 8 citations.

Topics: Engineering mathematics

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TL;DR: In this article, the use of matched asymptotic expansions in option pricing has been investigated in the context of stochastic processes of diffusion type. And a tentative framework for applied matched-asymptotics expansion applied directly to stochastically processes of the diffusion type is also proposed.

Abstract: Modern financial practice depends heavily on mathematics and a correspondingly large theory has grown up to meet this demand. This paper focuses on the use of matched asymptotic expansions in option pricing; it presents illustrations of the approach in ‘plain vanilla’ option valuation, in valuation using a fast mean-reverting-stochastic volatility model, and in a model for illiquid markets. A tentative framework for matched asymptotic expansions applied directly to stochastic processes of diffusion type is also proposed.

53 citations

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TL;DR: In this paper, the authors examined the fluid dynamics of capillary drawing using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary, and made predictions concerning the effects of fiber rotation.

Abstract: Understanding and controlling the manufacturing process of producing (“drawing”) microstructured optical fibres (“holey fibres”) is of paramount importance in obtaining optimal control of the final fibre geometry and identifying industrially useful production regimes. The high cost of the manufacturing process and the challenge of ensuring reproducible final fibre geometries renders theoretical approaches invaluable. In this study the fluid dynamics of capillary drawing is examined using an extensional-flow asymptotic approach based on the small aspect ratio of the capillary. The key focus of the study is the additional effects that may be introduced by adding fibre rotation to the manufacturing process. Predictions are made concerning the effects of rotation, and a variety of asymptotic limits are examined in order to gain an understanding of the physics involved. Drawing regimes that are useful from a practical point of view are identified and the role of fibre rotation, both as a control measure (that may be used to influence the final geometry of a capillary) and as a means of reducing unwanted effects (such as fibre birefringence and polarisation model dispersion), is discussed.

13 citations

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TL;DR: A model where geographic information, including licensed areas of primary users (PUs) and locations of secondary users (SUs), plays an important role in the spectrum sharing system and the existence and uniqueness of the evolutionary stable strategy quota vector of each PU is proved.

Abstract: For a spectrum sharing system using economic approaches, conventional models without geographic considerations are oversimplified. In this paper, we develop a model where geographic information, including licensed areas of primary users (PUs) and locations of secondary users (SUs), plays an important role in the spectrum sharing system. We consider a multi-price policy and the pricing power of non-cooperative PUs in multiple geographic areas. Meanwhile, the value assessment of a channel is price-related and the demand from the SUs is price-elastic. To maximize the payoffs of the PUs, we propose a unique quota transaction process. By applying an evolutionary procedure defined as replicator dynamics, we prove the existence and uniqueness of the evolutionary stable strategy quota vector of each PU, which leads to the optimal payoff for each PU selling channels without reserve. In the scenario of selling channels with reserve, we predict the channel prices for the PUs leading to the optimal supplies of the PUs and hence the optimal payoffs. Furthermore, we introduce a grouping mechanism to simplify the process. In our simulation, the effectiveness of the learning processes designed for the two scenarios is verified and our spectrum sharing scheme is shown efficient in utilizing the frequency resources.

8 citations

01 Jan 2010

TL;DR: The eect of a road block on the trac depends on three parameters, the density of the oncoming trac, the time T and the ratio of the speed limit in the road block to the speedlimit on the open road.

Abstract: The eect of a road block on trac ow is investigated using the model in which the trac velocity is a linear function of the trac density. The road consists of two lanes in one direction and one lane is closed for a short distance by a road block. The length of the tailback at the entrance to the road block, the time spent in the road block and the trac ux at the exit to the road block are calculated. The maximum length of the tailback is a linear function of the time T that the road block was in place. The eect of the road block on the trac depends on three parameters, the density of the oncoming trac, the time T and the ratio of the speed limit in the road block to the speed limit on the open road. The congestion caused by the road block can be managed by adjusting T and .

5 citations

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01 Jan 2010

TL;DR: In this article, the authors consider the regularity and approximation of a hyperbolic-elliptic coupled problem in a nonconvex, not simply connected domain Ω that is supposed to be homeomorph to an annular domain.

Abstract: In this thesis, we investigate the regularity and approximation of a hyperbolic-elliptic coupled problem. In particular, we consider the Poisson and the transport equation where both are assigned nonhomogeneous Dirichlet boundary conditions. The coupling of the two problems is executed as follows. The right hand side function of the Poisson equation is the solution ρ of the transport equation whereas the gradient field E = −∇u, with u being solution of the Poisson problem, is the convective field for the transport equation. The analysis is done throughout on a nonconvex, not simply connected domain Ω that is supposed to be homeomorph to an annular domain. In the first part of this thesis, we will focus on the existence and uniqueness of a classical solution to this highly nonlinear problem using the framework of Holder continuous functions. Herein, we distinguish between a time dependent and time independent formulation. In both cases, we investigate the streamline functions defined by the convective field E. These are used in the time dependent case to derive an operator equation whose fixed point is the streamline function to the gradient of the classical solution u. In the time independent setting, we formulate explicitly the solution operators L for the Poisson and T for the transport equation and show with a fixed point argument the existence and uniqueness of a classical solution (u, ρ). The second part of this thesis deals with the approximation of the coupled problem in Sobolev spaces. First, we show that the nonlinear transport equation can be formulated equivalently as variational inequality and analyse its Galerkin finite element discretization. Due to the nonlinearity of the coupled problem, it is necessary to use iterative solvers. We will introduce the staggered algorithm which is an iterative method solving alternating the Poisson and transport equation until convergence is obtained. Assuming that L◦T is a contraction in the Sobolev space H1(Ω), we will investigate the convergence of the discrete staggered algorithm and obtain an error estimate. Subsequently, we present numerical results in two and three dimensions. Beside the staggered algorithm, we will introduce other iterative solvers that are based on linearizing the coupled problem by Newton’s method. We illustrate that all iterative solvers converge satisfactorily to the solution (u, ρ).

5 citations