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Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

This book contains a collection of essays written by renowned economists on the occasion of Andras Brody's 70th birthday. Andras Brody has contributed to many fields of economics, including mathematical modelling, the theory of economic growth, marxian economics and input-output analysis. The essays contained in this book deal with new results in these and related fields, and cover both theoretical and empirical aspects. Among the topics being discussed are foundations of input-output analysis, methodologies for measuring economic growth and structural change, and normative aspects of economic behaviour. The book also includes a chapter on the extraordinary event of building an input-output table for the newly reunited Germany.

This book presents an extensive study on the effectiveness of recent regulations on pharmaceutical prices in India, exploring the weaknesses in the design and implementation of pharmaceutical price controls and investigating what can be done to fix the broken system. In addition, it examines the extent to which essential medicines are actually made affordable by price controls. The book argues that companies make the pharmaceutical price control regime largely ineffective by coordinating to increase pre-regulation prices; by diversifying horizontally away from the regulated markets and increasing prices in the unregulated markets; by manipulating trade margins; and by refusing to comply with the regulation because the penalties remains negligible. The book draws on extensive empirical research involving India’s 2013 Drug Price Control Order and widely-used medicines such as paracetamol and metformin to illustrate how firms have weakened regulation. It argues that theregulatory regime can be strengthened by using systematic analysis of product- and region-level data in the Indian pharmaceutical industry, and by screening for the strategies that firms currently employ to circumvent regulation. In closing, it discusses recent efforts to strengthen the implementation of price controls in India and expanding the scope of price controls to medical devices.

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Find Historically Inspired House Plans with Modern Floor Plans by Rhonda L. Cornell in Paperback and other formats in Architecture > Buildings - Residential.

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