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In modern financial practice, asset prices are modelled by means of stochastic processes, and continuous-time stochastic calculus thus plays a central role in financial modelling. This approach has its roots in the foundational work of the Nobel laureates Black, Scholes and Merton. Asset prices are further assumed to be rationalizable, that is, determined by equality of demand and supply on some market. This approach has its roots in the foundational work on General Equilibrium of the Nobel laureates Arrow and Debreu and in the work of McKenzie. This book has four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of general equilibrium theory, and applies this in financial markets. The last part is more advanced and tackles market incompleteness and the valuation of exotic options in a complete market.

Options (Finance) --- Equilibrium (Economics) --- Mathematical models. --- -332.0151955 --- Mathematical models --- Options (Finances) --- Equilibre (Economie politique) --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- 332.0151955 --- 305.91 --- AA / International- internationaal --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Economics, Mathematical . --- Probabilities. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Economics --- Mathematical economics --- Econometrics --- Methodology --- Options (Finance) - Mathematical models --- Equilibrium (Economics) - Mathematical models

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Although there are many books on mathematical finance, few deal with the statistical aspects of modern data analysis as applied to financial problems. This book fills this gap by addressing some of the most challenging issues facing any financial engineer. It shows how sophisticated mathematics and modern statistical techniques can be used in concrete financial problems. Concerns of risk management are addressed by the control of extreme values, the fitting of distributions with heavy tails, the computation of values at risk (VaR), and other measures of risk. Data description techniques such as principal component analysis (PCA), smoothing, and regression are applied to the construction of yield and forward curve. Nonparametric estimation and nonlinear filtering are used for option pricing and earnings prediction. The book is intended for undergraduate students majoring in financial engineering, or graduate students in a Master in finance or MBA program. Because it was designed as a teaching vehicle, it is sprinkled with practical examples using market data, and each chapter ends with exercises. Practical examples are solved in the computing environment of S-PLUS. They illustrate problems occurring in the commodity and energy markets, the fixed income markets as well as the equity markets, and even some new emerging markets like the weather markets. The book can help quantitative analysts by guiding them through the details of statistical model estimation and implementation. It will also be of interest to researchers wishing to manipulate financial data, implement abstract concepts, and test mathematical theories, especially by addressing practical issues that are often neglected in the presentation of the theory. Rene Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over seventy articles and six books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and he is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching of statistics, for research in signal analysis, and more recently, he contributed the library EVANESCE for the analysis of heavy tail distributions and copulas. The latter was included in the latest version of S-Plus. He has worked for many years on energy and weather derivatives, and he is recognized as a leading researcher and consultant in this area.

Private finance --- Mathematical statistics --- Finance --- Finance - General --- Business & Economics --- Mathematical models --- Econometric models --- -Finance --- -332.0151955 --- Funding --- Funds --- Economics --- Currency question --- S-Plus. --- SPlus --- Business. --- Business mathematics. --- Economics, Mathematical. --- Actuarial science. --- Computer mathematics. --- Statistics. --- Business and Management. --- Business Mathematics. --- Actuarial Sciences. --- Computational Mathematics and Numerical Analysis. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Quantitative Finance. --- Computer science --- Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Mathematics. --- Mathematical statistics. --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Mathematics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Computer mathematics --- Electronic data processing --- Statistics --- Insurance --- Arithmetic, Commercial --- Business --- Business arithmetic --- Business math --- Commercial arithmetic --- Methodology

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Mathematical statistics --- 519.2 --- 330.115 --- Finance --- -Time-series analysis --- -AA / International- internationaal --- 305.91 --- 305.7 --- 304.0 --- 303.0 --- -332.0151955 --- Funding --- Funds --- Economics --- Currency question --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Probabilities --- Probability. Mathematical statistics --- Econometrie --- Mathematical models --- Econometric models --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen. --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken). --- S-Plus. --- SPlus --- 330.115 Econometrie --- 519.2 Probability. Mathematical statistics --- Econometrics. --- Computer software. --- Programming languages (Electronic computers). --- Statistics . --- Economics, Mathematical . --- Mathematical Software. --- Programming Languages, Compilers, Interpreters. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Quantitative Finance. --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Electronic data processing --- Languages, Artificial --- Software, Computer --- Computer systems --- Economics, Mathematical --- Statistics --- Mathematical economics --- Econometrics --- Mathematics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Methodology --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Zuivere statistische analyse (algemene naslagwerken). Tijdreeksen --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- -Finance --- -Mathematical models