Business Versus Complexity

AbstractAccording to our view, business is an economic category consists of products that are sold in markets that have a significant contribution to a company's business portfolio. At a company's level, businesses have a competitive position in the distribution of its resources to the consumption of inputs. In terms of management decision the allocation of material resources, labor and capital reflects its market position and determine the hierarchy of the various products that have turnover. The cost of the Knowledge of information produced determine the internal complexity of operation at an organization. Complex business models started to be represented everywhere around us the relationships between various entities that adapt and respond to the dynamics of internal and external environment. Most often these models operate in networks. Information system (IS) can be a modern solution to explain the above-mentioned complexity. The information in this case to capture the interactions between production function and the marketing in a subsystem which dialogues between its parts that are found in the interaction within the system to create knowledge and value this knowledge in costs and outcome. This paper focuses on information systems in an organization of great complexity as Google. Inc. its financial accountancy consideration and also the effects measures of Information System (IS) used in Google Inc

Multilevel Monte Carlo methods

The author's presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity, flexibility and generality of the multilevel Monte Carlo approach. It also offers a few original ideas and suggests areas for future research

Randomized Complexity of Parametric Integration and the Role of Adaption I. Finite Dimensional Case

We study the randomized $n$-th minimal errors (and hence the complexity) of vector valued mean computation, which is the discrete version of parametric integration. The results of the present paper form the basis for the complexity analysis of parametric integration in Sobolev spaces, which will be presented in Part 2. Altogether this extends previous results of Heinrich and Sindambiwe (J.\ Complexity, 15 (1999), 317--341) and Wiegand (Shaker Verlag, 2006). Moreover, a basic problem of Information-Based Complexity on the power of adaption for linear problems in the randomized setting is solved.Comment: 30 page

An introduction to multilevel Monte Carlo for option valuation

Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation. In 2008, Giles proposed a remarkable improvement to the approach of discretizing with a numerical method and applying standard Monte Carlo. His multilevel Monte Carlo method offers an order of speed up given by the inverse of epsilon, where epsilon is the required accuracy. So computations can run 100 times more quickly when two digits of accuracy are required. The multilevel philosophy has since been adopted by a range of researchers and a wealth of practically significant results has arisen, most of which have yet to make their way into the expository literature. In this work, we give a brief, accessible, introduction to multilevel Monte Carlo and summarize recent results applicable to the task of option evaluation.Comment: Submitted to International Journal of Computer Mathematics, special issue on Computational Methods in Financ

Complexity of Initial Value Problems in Banach Spaces

We study the complexity of initial value problems for Banach space valued ordinary differential equations in the randomized setting. The right- hand side is assumed to be r-smooth, the r-th derivatives being ϱ-Hölder continuous. We develop and analyze a randomized algorithm. Furthermore, we prove lower bounds and thus obtain complexity estimates. They are related to the type of the underlying Banach space. We also consider the deterministic setting. The results extend previous ones for the finite dimensional case from [2, 9, 10].Изучается сложность задачи Коши для банаховозначных обыкновенных дифференциальных уравнений с рандомизированными начальными условиями. Правая часть предполагается r-гладкой, а r-е производные ϱ-гельдеровыми. Разрабатывается и анализируется рандомизированный алгоритм. Кроме того, доказываются оценки снизу и, таким образом, получаются оценки сложности. Они связаны с типом основного банахова пространства. Также рассматриваются детерминистические начальные данные. Эти результаты обобщают предыдущие, полученные для конечномерного случая [2, 9, 10]