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This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed. The new edition adds substantial material from current areas of active research, notably: a new chapter on coherent risk measures, with applications to hedging a complete proof of the first fundamental theorem of asset pricing for general discrete market models the arbitrage interval for incomplete discrete-time markets characterization of complete discrete-time markets, using extended models risk and return and sensitivity analysis for the Black-Scholes model The treatment remains careful and detailed rather than comprehensive, with a clear focus on options. From here the reader can progress to the current research literature and the use of similar methods for more exotic financial instruments. The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measure-theoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets and credit institutions is based. The first edition has been used successfully in a wide range of Master's programs in mathematical finance and this new edition should prove even more popular in this expanding market. It should equally be useful to risk managers and practitioners looking to master the mathematical tools needed for modern pricing and hedging techniques. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary, having held positions in mathematics at the University of Alberta, Hull, Oxford, Warwick, and Northwestern. He is the author of over 300 research papers and several books, including Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and, with Lakhdar Aggoun, Measure Theory and Filtering: Theory and Applications. He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications and the Canadian Applied Mathematics Quarterly. P. Ekkehard Kopp is Professor of Mathematics, and a former Pro-Vice-Chancellor, at the University of Hull. He is the author of Martingales and Stochastic Integrals, Analysis and, with Marek Capinski, of Measure, Integral and Probability. He is a member of the Editorial Board of Springer Finance.

Investments --- Stochastic analysis. --- Options (Finance) --- Securities --- Mathematics. --- Mathematical models. --- Prices --- Stochastic analysis --- 305.91 --- AA / International- internationaal --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Blue sky laws --- Capitalization (Finance) --- Investment securities --- Portfolio --- Scrip --- Securities law --- Underwriting --- Investment banking --- Mathematics of investment --- Business mathematics --- Mathematics --- Mathematical models --- Prices&delete& --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Law and legislation --- Money market. Capital market --- International finance --- Mathematical statistics

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Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods, whereas the second half discusses model-specific algorithms. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value. Søren Asmussen is a professor of Applied Probability at Aarhus University, Denmark and Peter Glynn is the Thomas Ford professor of Engineering at Stanford University.

Simulation methods --- Stochastic analysis --- 519.2 --- 519.245 --- 681.3*G3 --- Simulation techniques --- System simulation --- Operations research --- Systems engineering --- Models and modelmaking --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- 681.3*G3 Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- 519.245 Stochastic approximation. Monte Carlo methods --- Stochastic approximation. Monte Carlo methods --- Analyse stochastique --- Méthodes de simulation --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Stochastic analysis. --- Simulation methods. --- Distribution (Probability theory. --- Mathematical statistics. --- Operations research. --- Industrial engineering. --- Finance. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Operations Research/Decision Theory. --- Industrial and Production Engineering. --- Operations Research, Management Science. --- Quantitative Finance. --- Funding --- Funds --- Economics --- Currency question --- Management engineering --- Simplification in industry --- Engineering --- Value analysis (Cost control) --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistical methods --- Probabilities. --- Statistics . --- Decision making. --- Production engineering. --- Management science. --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Quantitative business analysis --- Management --- Problem solving --- Statistical decision --- Manufacturing engineering --- Process engineering --- Mechanical engineering --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management decisions --- Choice (Psychology) --- Statistical analysis --- Statistical data --- Statistical science --- Probability --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Decision making