قیمت‌گذاری گزینه‌ها و بهینه‌سازی پرتفوی: روش‌های مدرن ریاضیات مالی (تحصیلات تکمیلی در ریاضیات)

Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of the purely mathematical topics are treated in extended “excursions” from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential. Especially useful for students seeking a lively introduction to Itô calculus. —Short Book Reviews, International Statistical Institute

Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Ito calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of the purely mathematical topics are treated in extended ''excursions'' from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential. Especially useful for students seeking a lively introduction to Ito calculus. —Short Book Reviews, International Statistical Institute

Understanding And Working With The Current Models Of Financial Markets Requires A Sound Knowledge Of The Mathematical Tools And Ideas From Which They Are Built. Banks And Financial Houses All Over The World Recognize This And Are Avidly Recruiting Mathematicians, Physicists, And Other Scientists With These Skills. The Mathematics Involved In Modern Finance Springs From The Heart Of Probability And Analysis, For Example: The It Calculus, Stochastic Control, Differential Equations, And Martingales. The Authors Give Rigorous Treatments Of These Topics, While Always Keeping The Applications In Mind. Thus, The Way In Which The Mathematics Is Developed Is Governed By The Way It Will Be Used, Rather Than By The Goal Of Optimal Generality. Indeed, Most Of Purely Mathematical Topics Are Treated In Extended Excursions From The Applications Into The Theory. Thus, With The Main Topic Of Financial Modelling And Optimization In View, The Reader Also Obtains A Self-contained And Complete Introduction To The Underlying Mathematics. This Book Is Specifically Designed As A Graduate Textbook. Introduces Ito calculus, concentrating on applications in financial mathematics. Builds the standard diffusion type security market model, then treats the pricing of options in detail, introducing the method of option pricing via replication and no arbitrage. Presents a method of pricing options with partial differential equations, and presents examples of exotic options. Describes basics of Monte Carlo methods, tree methods, and finite difference methods, and deals with the martingale method and the stochastic control method for portfolio optimization. Assumes a previous basic course in probability theory. Author information is not given. Annotation c. Book News, Inc., Portland, OR (booknews.com) Understanding and working with the models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Covering the topic of financial modelling and optimization, this book helps readers obtain a self-contained introduction to the underlying mathematics. It is suitable as a graduate textbook. Before we shall consider continuous-time market models, we start by looking at a simple one-period model.