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Logarithmic Factor (logarithmic + factor)

Distribution by Scientific Domains
Mathematics and Statistics75%

Selected Abstracts

CRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODEL

MATHEMATICAL FINANCE, Issue 3 2005
Etienne ChevalierArticle first published online: 10 JUN 200
We consider an American put option on a dividend-paying stock whose volatility is a function of the stock value. Near the maturity of this option, an expansion of the critical stock price is given. If the stock dividend rate is greater than the market interest rate, the payoff function is smooth near the limit of the critical price. We deduce an expansion of the critical price near maturity from an expansion of the value function of an optimal stopping problem. It turns out that the behavior of the critical price is parabolic. In the other case, we are in a less regular situation and an extra logarithmic factor appears. To prove this result, we show that the American and European critical prices have the same first-order behavior near maturity. Finally, in order to get an expansion of the European critical price, we use a parity formula for exchanging the strike price and the spot price in the value functions of European puts. [source]

Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction,diffusion problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2008
Guoqing Zhu
Abstract The numerical approximation by a lower-order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi-optimal-order error estimates are proved in the ,-weighted H1 -norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in ,-weighted H1 -norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Approximation algorithms for general one-warehouse multi-retailer systems

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2009
Zuo-Jun Max Shen
Abstract Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross-docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ,-optimality can be obtained by solving a related piece-wise linear concave cost multi-commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ,) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece-wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece-wise concavity feature of the cost functions. This gives rise to a unified and generic LP-based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source]

Coloring H-free hypergraphs

RANDOM STRUCTURES AND ALGORITHMS, Issue 1 2010
Tom Bohman
Abstract Fix r , 2 and a collection of r -uniform hypergraphs . What is the minimum number of edges in an -free r -uniform hypergraph with chromatic number greater than k? We investigate this question for various . Our results include the following: An (r,l)-system is an r -uniform hypergraph with every two edges sharing at most l vertices. For k sufficiently large, there is an (r,l)-system with chromatic number greater than k and number of edges at most c(kr,1 log k)l/(l,1), where This improves on the previous best bounds of Kostochka et al. (Random Structures Algorithms 19 (2001), 87,98). The upper bound is sharp apart from the constant c as shown in (Random Structures Algorithms 19 (2001) 87,98). The minimum number of edges in an r -uniform hypergraph with independent neighborhoods and chromatic number greater than k is of order kr+1/(r,1) log O(1)k as k , ,. This generalizes (aside from logarithmic factors) a result of Gimbel and Thomassen (Discrete Mathematics 219 (2000), 275,277) for triangle-free graphs. Let T be an r -uniform hypertree of t edges. Then every T -free r -uniform hypergraph has chromatic number at most 2(r , 1)(t , 1) + 1. This generalizes the well-known fact that every T -free graph has chromatic number at most t. Several open problems and conjectures are also posed. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010 [source]