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Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. The subject draws upon quite difficult results from the theory of stochastic processes, stochastic calculus and differential equations, among others, which can be daunting for the beginning researcher. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The authors proceed by successive generalisations with increasing complexity assuming some basic knowledge of probability theory. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.

Quantitative methods (economics) --- financiële analyse --- Operational research. Game theory --- kansrekening --- Financial analysis --- financiën --- Finance --- stochastische analyse --- Finances --- Mathematical models --- Modèles mathématiques --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Mathematical models. --- Public finance. --- Mathematics. --- Finance. --- Distribution (Probability theory. --- Public Economics. --- Applications of Mathematics. --- Quantitative Finance. --- Finance, general. --- Probability Theory and Stochastic Processes. --- Math --- Science --- Cameralistics --- Public finance --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Funding --- Funds --- Economics --- 332.015195 --- 303.0 --- 305.91 --- 51 --- AA / International- internationaal --- Statistische technieken in econometrie. Wiskundige statistiek (algemene werken en handboeken) --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Wiskunde --- Public finances --- Applied mathematics. --- Engineering mathematics. --- Economics, Mathematical . --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Mathematical economics --- Econometrics --- Engineering --- Engineering analysis --- Mathematical analysis --- Methodology --- Finance - Mathematical models