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This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.

Statistical science --- Operational research. Game theory --- Probability theory --- waarschijnlijkheidstheorie --- stochastische analyse --- statistiek --- kansrekening --- statistisch onderzoek --- Options (Finance) --- Stochastic analysis. --- Anàlisi estocàstica --- Opcions (Finances)

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Now in its fifth edition, Derivatives and Internal Models provides a comprehensive and thorough introduction to derivative pricing, risk management and portfolio optimization, covering all relevant topics with enough hands-on, depth of detail to enable readers to develop their own pricing and risk tools. The book provides insight into modern market risk quantification methods such as variance-covariance, historical simulation, Monte Carlo, hedge ratios, etc., including time series analysis and statistical concepts such as GARCH Models or Chi-Square-distributions. It shows how optimal trading decisions can be deduced once risk has been quantified by introducing risk-adjusted performance measures and a complete presentation of modern quantitative portfolio optimization. Furthermore, all the important modern derivatives and their pricing methods are presented; from basic discounted cash flow methods to Black-Scholes, binomial trees, differential equations, finite difference schemes, Monte Carlo methods, Martingales and Numeraires, terms structure models, etc. The fifth edition of this classic finance book has been comprehensively reviewed. New chapters/content cover multicurve bootstrapping, the valuation and hedging of credit default risk that is inherently incorporated in every derivative—both of which are direct and permanent consequences of the financial crises with a large impact on our understanding of modern derivative valuation. The book will be accompanied by downloadable Excel spread sheets, which demonstrate how the theoretical concepts explained in the book can be turned into valuable algorithms and applications and will serve as an excellent starting point for the reader’s own bespoke solutions for valuation and risk management systems.

Capital market. --- Risk management. --- Accounting. --- Economics. --- Corporations-Finance. --- Investment banking. --- Securities. --- Capital Markets. --- Risk Management. --- Accounting/Auditing. --- Economics, general. --- Corporate Finance. --- Investments and Securities. --- Blue sky laws --- Capitalization (Finance) --- Investment securities --- Portfolio --- Scrip --- Securities --- Securities law --- Underwriting --- Investments --- Investment banking --- Banks and banking, Investment --- Investment banks --- Financial institutions --- Economic theory --- Political economy --- Social sciences --- Economic man --- Accountancy --- Business enterprises --- Commerce --- Commercial accounting --- Finance --- Financial accounting --- Business --- Bookkeeping --- Insurance --- Management --- Capital markets --- Market, Capital --- Loans --- Money market --- Crowding out (Economics) --- Efficient market theory --- Law and legislation --- Accounting --- Bookkeeping . --- Management science. --- Corporations—Finance. --- Quantitative business analysis --- Problem solving --- Operations research --- Statistical decision --- Double entry bookkeeping --- Business education --- Gestió del risc --- Risc (Economia) --- Actius financers derivats --- Risc --- Economia --- Avaluació del risc --- Percepció del risc --- Risc (Assegurances) --- Risc de crèdit --- Beneficis --- Probabilitats --- Assegurances --- Actius derivats (Finances) --- Derivats financers --- Instruments derivats (Finances) --- Instruments financers derivats --- Nous instruments financers --- Nous productes financers --- Productes financers derivats --- Finances --- Valors --- Futurs financers --- Opcions (Finances) --- Swaps

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This text provides an accessible introduction to the classical mathematical underpinnings of modern finance. Professor Björk concentrates on the probabilistic theory of continuous arbitrage pricing of financial derivatives.

Arbitrage. --- Arbitrage --- Arbitrage - Mathematical models --- Derivative securities - Mathematical models --- Securities --- Speculation --- Law and legislation --- Arbitratge (Borsa) --- Economia matemàtica --- Integrals estocàstiques --- Teoria de control --- Actius financers derivats --- Models economètrics --- Models matemàtics --- Martingales (Matemàtica) --- Processos estocàstics --- Càlcul estocàstic --- Funcions aleatòries --- Processos aleatoris --- Probabilitats --- Anàlisi estocàstica --- Aproximació estocàstica --- Camps aleatoris --- Filtre de Kalman --- Fluctuacions (Física) --- Mètode de Montecarlo --- Processos de Markov --- Processos de ramificació --- Processos gaussians --- Processos puntuals --- Rutes aleatòries (Matemàtica) --- Semimartingales (Matemàtica) --- Sistemes estocàstics --- Teoremes de límit (Teoria de probabilitats) --- Teoria de cues --- Teoria de l'estimació --- Teoria de la predicció --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Modelització multiescala --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Models econòmics --- Econometria --- Actius derivats (Finances) --- Derivats financers --- Instruments derivats (Finances) --- Instruments financers derivats --- Nous instruments financers --- Nous productes financers --- Productes financers derivats --- Finances --- Valors --- Futurs financers --- Opcions (Finances) --- Swaps --- Control (Matemàtica) --- Control òptim --- Regulació --- Control automàtic --- Sistemes de control biològic --- Integració estocàstica --- Matemàtica econòmica --- Arbitratge (Economia) --- Arbitratge (Finances) --- Abritratge financer --- Borsa de valors --- Especulació --- Derivative securities

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Artificial intelligence --- Financial applications. --- Finance --- Data processing --- Inversions --- Estadística matemàtica --- Intel·ligència artificial --- Ciència cognitiva --- Mètodes de simulació --- Processament de dades --- Sistemes autoorganitzatius --- Aprenentatge automàtic --- Demostració automàtica de teoremes --- Intel·ligència artificial distribuïda --- Intel·ligència computacional --- Sistemes adaptatius --- Tractament del llenguatge natural (Informàtica) --- Raonament qualitatiu --- Representació del coneixement (Teoria de la informació) --- Sistemes de pregunta i resposta --- Traducció automàtica --- Visió per ordinador --- Xarxes neuronals (Informàtica) --- Xarxes semàntiques (Teoria de la informació) --- Agents intel·ligents (Programes d'ordinador) --- Programació per restriccions --- Vida artificial --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Estadística --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística) --- Inversions de capital --- Capital --- Accions (Borsa) --- Assignació d'actius --- Bons --- Capital de risc --- Inversions bancàries --- Inversions immobiliàries --- Inversions públiques --- Opcions (Finances) --- Rendibilitat --- Mercat de futurs --- Societats d'inversió --- Valors --- Estalvi