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Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.

Institutional investments -- Management. --- Investment advisors -- Marketing. --- Investment analysis --- Merton Model --- Business & Economics --- Economic Theory --- Mathematical models --- Merton Model. --- Mathematical models. --- Asset Value Model --- Mathematics. --- Finance. --- Economics, Mathematical. --- Numerical analysis. --- Calculus of variations. --- Probabilities. --- Quantitative Finance. --- Finance, general. --- Numerical Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Probability Theory and Stochastic Processes. --- Business failures --- Mathematical optimization. --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical . --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of --- Mathematical economics --- Econometrics --- Methodology

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Numerical Methods in Finance has recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. This book, based on lectures given at the Newton Institute as part of a broader program, describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially of American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures; identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Articles have been written in a pedagogic style and made reasonably self-contained, covering both mathematical matters and practical issues in numerical problems. Thus the book has something to offer economists, probabilists and applied mathematicians working in finance, for all of whom this will be the only up-to-date reference on the subject.

Finance --- Finances --- Mathematical models. --- Modèles mathématiques --- Modèles mathématiques --- Numerical methods of optimisation --- -Probability. Mathematical statistics --- -336.7 Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- 336.7 --- 519.2 --- 336.7 Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- Geldwezen. Kredietwezen. Bankwezen. Financien. Monetaire econonomie. Beurswezen --- 519.2 Probability. Mathematical statistics --- Probability. Mathematical statistics --- Mathematical models --- Stochastic processes --- International financial management --- Congresses --- Finance - Mathematical models

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Martingales (Mathematics) --- Diffusion processes --- Markov processes --- Processus de diffusion --- Diffusion processes. --- Markov processes. --- Martingales (Mathematics). --- Markov, Processus de --- Martingales (Mathématiques)

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This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

Diffusion processes. --- Markov processes. --- Martingales (Mathematics)

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