Author

# Sam Howison

Bio: Sam Howison is an academic researcher from University of Oxford. The author has contributed to research in topics: Valuation of options & Electronic trading. The author has an hindex of 43, co-authored 160 publications receiving 7551 citations.

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TL;DR: In this paper, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation, and present a unified approach to modelling derivative products as partial differential equations using numerical solutions where appropriate.

Abstract: Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant 'real-world' mathematics. In this book the authors describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation. A unified approach to modelling derivative products as partial differential equations is presented, using numerical solutions where appropriate. Some mathematics is assumed, but clear explanations are provided for material beyond elementary calculus, probability, and algebra. Over 140 exercises are included. This volume will become the standard introduction to this exciting new field for advanced undergraduate students.

752 citations

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29 Sep 1995TL;DR: In this article, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation, and present a unified approach to modelling derivative products as partial differential equations using numerical solutions where appropriate.

Abstract: Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods; the area is an expanding source for novel and relevant 'real-world' mathematics. In this book the authors describe the modelling of financial derivative products from an applied mathematician's viewpoint, from modelling through analysis to elementary computation. A unified approach to modelling derivative products as partial differential equations is presented, using numerical solutions where appropriate. Some mathematics is assumed, but clear explanations are provided for material beyond elementary calculus, probability, and algebra. Over 140 exercises are included. This volume will become the standard introduction to this exciting new field for advanced undergraduate students.

535 citations

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TL;DR: In this article, a model for a class of water-entry problems characterized by the geometrical property that the impacting body is nearly parallel to the undisturbed water surface and that the impact is so rapid that gravity can be neglected is presented.

Abstract: This paper summarizes and extends some mathematical results for a model for a class of water-entry problems characterized by the geometrical property that the impacting body is nearly parallel to the undisturbed water surface and that the impact is so rapid that gravity can be neglected. Explicit solutions for the pressure distributions are given in the case of two-dimensional flow and a variational formulation is described which provides a simple numerical algorithm for three-dimensional flows. We also pose some open questions concerning the well-posedness and physical relevance of the model for exit problems or when there is an air gap between the impacting body and the water.

295 citations

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TL;DR: A survey of empirical and theoretical studies of limit order books can be found in this article. But, the authors highlight several key unresolved questions about LOBs, and also illustrate that many such models poorly resemble real LBOs and that several well-established empirical facts have yet to be reproduced satisfactorily.

Abstract: Limit order books (LOBs) match buyers and sellers in more than half of the world’s financial markets. This survey highlights the insights that have emerged from the wealth of empirical and theoretical studies of LOBs. We examine the findings reported by statistical analyses of historical LOB data and discuss how several LOB models provide insight into certain aspects of the mechanism. We also illustrate that many such models poorly resemble real LOBs and that several well-established empirical facts have yet to be reproduced satisfactorily. Finally, we identify several key unresolved questions about LOBs.

216 citations

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2,345 citations

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01 Oct 1948

TL;DR: In this article, it was shown that a metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

Abstract: IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

2,042 citations

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TL;DR: The Arrow-Pratt theory of risk aversion was shown to be isomorphic to the theory of optimal choice under risk in this paper, making possible the application of a large body of knowledge about risk aversion to precautionary saving.

Abstract: The theory of precautionary saving is shown in this paper to be isomorphic to the Arrow-Pratt theory of risk aversion, making possible the application of a large body of knowledge about risk aversion to precautionary saving, and more generally, to the theory of optimal choice under risk In particular, a measure of the strength of precautionary saving motive analogous to the Arrow-Pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving, and to give a new interpretation of the Oreze-Modigliani substitution effect

1,944 citations