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Speculation --- Arbitrage --- Hedging (Finance) --- Mathematical models --- Mathematical models. --- 336.76 --- 336.76 Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- Beurswezen. Geldmarkt. Valutamarkt. Binnenlandse geldmarkt. Valutamarkt --- Private finance --- Actuarial mathematics --- Prices --- Speculation - Mathematical models --- Arbitrage - Mathematical models --- Hedging (Finance) - Mathematical models

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This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.

Arbitrage -- Mathematical models. --- Differential equations, Partial. --- Martingales (Mathematics). --- Options (Finance) -- Prices -- Mathematical models. --- Business & Economics --- Finance --- Economic Theory --- Investment & Speculation --- Options (Finance) --- Arbitrage --- Martingales (Mathematics) --- Prices --- Mathematical models. --- Partial differential equations --- Law and legislation --- Mathematics. --- Finance. --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical. --- Probabilities. --- Quantitative Finance. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Finance, general. --- Stochastic processes --- Securities --- Speculation --- Distribution (Probability theory. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Engineering --- Engineering analysis --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Methodology

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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