A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

A systematic methodology to assess the impact of human factors in ship design

Evaluating ship layout for human factors (HF) issues using simulation software such as maritimeEXODUS can be a long and complex process. The analysis requires the identification of relevant evaluation scenarios; encompassing evacuation and normal operations; the development of appropriate measures which can be used to gauge the performance of crew and vessel and finally; the interpretation of considerable simulation data. Currently, the only agreed guidelines for evaluating HFs performance of ship design relate to evacuation and so conclusions drawn concerning the overall suitability of a ship design by one naval architect can be quite different from those of another. The complexity of the task grows as the size and complexity of the vessel increases and as the number and type of evaluation scenarios considered increases. Equally, it can be extremely difficult for fleet operators to set HFs design objectives for new vessel concepts. The challenge for naval architects is to develop a procedure that allows both accurate and rapid assessment of HFs issues associated with vessel layout and crew operating procedures. In this paper we present a systematic and transparent methodology for assessing the HF performance of ship design which is both discriminating and diagnostic. The methodology is demonstrated using two variants of a hypothetical naval ship.

Triterpenoid saponins from a cytotoxic root extract of Sideroxylon foetidissimum subsp. gaumeri

Evaluation of the cytotoxicity of an ethanolic root extract of Sideroxylonfoetidissimum subsp. gaumeri (Sapotaceae) revealed activity against the murine macrophage-like cell line RAW 264.7. Systematic bioassay-guided fractionation of this extract gave an active saponin-containing fraction from which four saponins were isolated. Use of 1D ((1)H, (13)C, DEPT135) and 2D (COSY, TOCSY, HSQC, and HMBC) NMR, mass spectrometry and sugar analysis gave their structures as 3-O-(beta-D-glucopyranosyl-(1-->6)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, 3-O-beta-D-glucopyranosyl-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, 3-O-(beta-D-glucopyranosyl-(1-->6)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)-beta-D-xylopyranosyl-(1-->4)[beta-D-apiofuranosyl-(1-->3)]-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, and the known compound, 3-O-beta-D-glucopyranosyl-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-protobassic acid. Two further saponins were obtained from the same fraction, but as a 5:4 mixture comprising 3-O-(beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)-beta-D-xylopyranosyl-(1-->4)[beta-D-apiofuranosyl-(1-->3)]-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid and 3-O-(beta-D-apiofuranosyl-(1-->3)-beta-D-glucopyranosyl)-28-O-(alpha-L-rhamnopyranosyl-(1-->3)[beta-D-xylopyranosyl-(1-->4)]-beta-D-xylopyranosyl-(1-->4)-alpha-L-rhamnopyranosyl-(1-->2)-alpha-L-arabinopyranosyl)-16alpha-hydroxyprotobassic acid, respectively. This showed greater cytotoxicity (IC(50)=11.9+/-1.5 microg/ml) towards RAW 264.7 cells than the original extract (IC(50)=39.5+/-4.1 microg/ml), and the saponin-containing fraction derived from it (IC(50)=33.7+/-6.2 microg/ml).