Boundary number

The goal of this book is to develop robust, accurate and efficient numerical methods to price a number of derivative products in quantitative finance.We focus on onefactor and multifactor models for a wide range of derivative products such as options, fixed income products, interest rate products and ‘real’ options. Due to the complexity of these products it is very difficult to find exact or closed solutions for the pricing functions. Even if a closed solution can be found it may be very difficult to compute. For this and other reasons we need to resort to approximate methods.
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Projects have been in existence for thousands of years, dating back as far as Egyptian civilization and the construction of the pyramids. It is only recently that project management practices have evolved to the status of a discipline with proper methodology, tools, and techniques. Today, the need for efficient and effective management of projects within the organization comes about as a result of the increased competition in the marketplace.
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Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a freeboundary partial differential equation.
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ON A BOUNDARY VALUE PROBLEM FOR NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS ROBERT HAKL Received 21 August 2004 and in revised form 1 March 2005 We consider the problem u (t) = H(u)(t) + Q(u)(t), u(a) = h(u), where H,Q : C([a,b];R) αβ → L([a,b];R) are, in general, nonlinear continuous operators, H ∈ ab (g0 ,g1 , p0 , p1 ), and h : C([a,b];R) → R is a continuous functional. Eﬃcient conditions suﬃcient for the solvability and unique solvability of the problem considered are established. 1.
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Effective solutions to water quality challenges exist and have been implemented in a number of places. It is time for a global focus on protecting and improving the quality of the world’s freshwater resources. There are three fundamental solutions to water quality problems: (1) prevent pollution; (2) treat polluted water; and (3) restore ecosystems.
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In writing this book we received help from a number of people. We would like to thank in particular David Althus, Kier Ashton, Cate Banks, Robert Burrell, Jeremy Hopgood, and Katie O'Rourke for help with the research; Robert Burrell, Bill Cornish, Shaun McVeigh, Alain Pottage, Alain Strowel, Julian Thomas, Adam Tomkins, and Leanne Wiseman for reading and commenting on drafts; Virginia Catmur of Cambridge University Press for copyediting the typescript; and King's College Research Strategy Fund and the Institute of Advanced Legal Studies External Research Fund for ®nancial support....
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Now in its tenth year, the Internet Crime Complaint Center (IC3) has become a vital resource for victims of online crime and for law enforcement investigating and prosecuting offenders. In 2010, IC3 received the secondhighest number of complaints since its inception. IC3 also reached a major milestone this year when it received its twomillionth complaint. On average, IC3 receives and processes 25,000 complaints per month. IC3 is more than a repository for victim complaints.
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Solving PDEs generally means you must take the time to set up the underlying equations, material properties, and boundary conditions for a given problem. COMSOL Multiphysics, however, relieves you of much of this work. The package provides a number of application modes that consist of predefined templates and user interfaces already set up with equations and variables for specific areas of physics. Special properties allow the selection of, for instance, analysis type and model formulations.
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This type of coatings is also characterized with a large number of grain boundaries with a crystalline/amorphous transition across grain–matrix interfaces, restricting the rise and development of cracks. Such mechanism explains the resistance to fragile cracking of nanocomposite coatings (Veprek, 1997; Veprek, 1998; Rafaja et al., 2006).
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Consumer protection law and criminal law have both received considerable analysis from academic lawyers. The role of legal intervention with the aim of protecting the consumer has come in for scrutiny in a number of seminal works, many of which concentrate upon the role of consumer law in the marketplace. The role of criminal law has also been discussed by a large number of leading commentators, with particular attention being paid to the boundaries of criminal sanctions, and particular concern being addressed to increasing criminalisation.
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When seen from space, “Planet Earth” is a mix of clouds, with the majority (two thirds) of the total surface under ocean water with the remaining third of land forming what we call continents, with various degrees of increasing albedo from open water bodies, vegetation, bare soil, rocks, deserts, and snow/ice packs. In a very short time (relative to Earth's age), the modern human civilization has conquered its neighboring space with probes, satellites, and vehicles carrying humans for exploration.
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The impact of an earthquake, flood or war on reproductive health can be devastating. Communities in crisis are suddenly deprived of reproductive health information and services. Access is cut off, yet needs persist, even escalate. A large number of refugees and internally displaced women will be pregnant, facing delivery under dangerous conditions; others may be victims of violence including rape. The United Nations Population Fund (UNFPA) is committed to assisting and protecting women, men and youth made vulnerable by natural disaster, armed conflict, persecution and other causes.
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Let T (x, ε) denote the ﬁrst hitting time of the disc of radius ε centered at x for Brownian motion on the two dimensional torus T2 . We prove that supx∈T2 T (x, ε)/ log ε2 → 2/π as ε → 0. The same applies to Brownian motion on any smooth, compact connected, twodimensional, Riemannian manifold with unit area and no boundary. As a consequence, we prove a conjecture, due to Aldous (1989), that the number of steps it takes a simple random walk to cover all points of the lattice torus Z2 is asymptotic to 4n2 (log...
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The World Wide Web, for much of its existence, has been a method for distributing passive information to a widely distributed number of people. The Web has, indeed, been exceptionally good for that purpose. With the addition of forms and image maps, Web pages began to become interactive—but the interaction was often simply a new way to get at the same information. The limitations of Web distribution were all too apparent once designers began to try to stretch the boundaries of what the Web can do.
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The designations employed and the presentation of the material in this publication do not imply the expression of any opinion whatsoever on the part of the Secretariat of the United Nations concerning the legal status of any country, territory, city or area, or of its authorities, or concerning the delimitation of its frontiers or boundaries. Material in this publication may be freely quoted or reprinted, but full acknowledgement is requested, together with a reference to the document number.
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In this paper we will discuss the geometry of ﬁnite topology properly embedded minimal surfaces M in R3 . M of ﬁnite topology means M is homeomorphic to a compact surface M (of genus k and empty boundary) minus a ﬁnite number of points p1 , ..., pj ∈ M , called the punctures. A closed neighborhood E of a puncture in M is called an end of M . We will choose the ends suﬃciently small so they are topologically S 1 × [0, 1) and hence, annular. We remark that M is orientable since M is properly...
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Mapping Service Requirements to Network Resources The ability to properly map services to network resources in a multiservice network is highly important both for making the initial conﬁguration of a network domain, and also as a basis for performing network conﬁguration optimization. The basic task in both cases is the same, although in the latter case there is an initial conﬁguration to start with, as well as potentially a larger number of existing boundary conditions for the new conﬁguration.
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EIGENSTRUCTURE OF NONSELFADJOINT COMPLEX DISCRETE VECTOR STURMLIOUVILLE PROBLEMS ´ RAFAEL J. VILLANUEVA AND LUCAS JODAR Received 15 March 2004 and in revised form 5 June 2004 We present a study of complex discrete vector SturmLiouville problems, where coeﬃcients of the diﬀerence equation are complex numbers and the strongly coupled boundary conditions are nonselfadjoint. Moreover, eigenstructure, orthogonality, and eigenfunctions expansion are studied. Finally, an example is given. 1.
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MULTIPLICITY RESULTS FOR A CLASS OF ASYMMETRIC WEAKLY COUPLED SYSTEMS OF SECONDORDER ORDINARY DIFFERENTIAL EQUATIONS FRANCESCA DALBONO AND P. J. MCKENNA Received 1 November 2004 We prove the existence and multiplicity of solutions to a twopoint boundary value problem associated to a weakly coupled system of asymmetric secondorder equations. Applying a classical change of variables, we transform the initial problem into an equivalent problem whose solutions can be characterized by their nodal properties.
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This approach has inherent limitations, including its depends on assumptions about the material and boundary conditions. the assumptions can be minimized through diagnostic load test (Schulz, 1993, Goble et al. 1990 and 1992). This approach combines stress response under load conditions is known with the model number of the bridge. The difference between the approach to the assessment of civil structures and other structures system discussed earlier is huge.
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