Financial Markets In Continuous Time
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| Author | : Rose-Anne Dana |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2007-06-30 |
| Genre | : Mathematics |
| ISBN | : 3540711503 |
This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets (the Black-Scholes formula and its extensions), for optimal portfolio and consumption choice, and for obtaining the yield curve and pricing interest rate products. The third part recalls some concepts and results of equilibrium theory and applies this in financial markets. The last part tackles market incompleteness and the valuation of exotic options.
| Author | : Bernard Dumas |
| Publisher | : MIT Press |
| Total Pages | : 641 |
| Release | : 2017-10-27 |
| Genre | : Business & Economics |
| ISBN | : 0262036541 |
An introduction to economic applications of the theory of continuous-time finance that strikes a balance between mathematical rigor and economic interpretation of financial market regularities. This book introduces the economic applications of the theory of continuous-time finance, with the goal of enabling the construction of realistic models, particularly those involving incomplete markets. Indeed, most recent applications of continuous-time finance aim to capture the imperfections and dysfunctions of financial markets—characteristics that became especially apparent during the market turmoil that started in 2008. The book begins by using discrete time to illustrate the basic mechanisms and introduce such notions as completeness, redundant pricing, and no arbitrage. It develops the continuous-time analog of those mechanisms and introduces the powerful tools of stochastic calculus. Going beyond other textbooks, the book then focuses on the study of markets in which some form of incompleteness, volatility, heterogeneity, friction, or behavioral subtlety arises. After presenting solutions methods for control problems and related partial differential equations, the text examines portfolio optimization and equilibrium in incomplete markets, interest rate and fixed-income modeling, and stochastic volatility. Finally, it presents models where investors form different beliefs or suffer frictions, form habits, or have recursive utilities, studying the effects not only on optimal portfolio choices but also on equilibrium, or the price of primitive securities. The book strikes a balance between mathematical rigor and the need for economic interpretation of financial market regularities, although with an emphasis on the latter.
| Author | : Robert C. Merton |
| Publisher | : Wiley-Blackwell |
| Total Pages | : 754 |
| Release | : 1992-11-03 |
| Genre | : Business & Economics |
| ISBN | : 9780631185086 |
Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.
| Author | : Fabio Fornari |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 168 |
| Release | : 2000-05-31 |
| Genre | : Business & Economics |
| ISBN | : 9780792378426 |
Presenting advanced topics in financial econometrics and theoretical finance, this guide is divided into three main parts.
| Author | : Santiago Moreno-Bromberg |
| Publisher | : Princeton University Press |
| Total Pages | : 176 |
| Release | : 2018-01-08 |
| Genre | : Business & Economics |
| ISBN | : 1400889200 |
Continuous-Time Models in Corporate Finance synthesizes four decades of research to show how stochastic calculus can be used in corporate finance. Combining mathematical rigor with economic intuition, Santiago Moreno-Bromberg and Jean-Charles Rochet analyze corporate decisions such as dividend distribution, the issuance of securities, and capital structure and default. They pay particular attention to financial intermediaries, including banks and insurance companies. The authors begin by recalling the ways that option-pricing techniques can be employed for the pricing of corporate debt and equity. They then present the dynamic model of the trade-off between taxes and bankruptcy costs and derive implications for optimal capital structure. The core chapter introduces the workhorse liquidity-management model—where liquidity and risk management decisions are made in order to minimize the costs of external finance. This model is used to study corporate finance decisions and specific features of banks and insurance companies. The book concludes by presenting the dynamic agency model, where financial frictions stem from the lack of interest alignment between a firm's manager and its financiers. The appendix contains an overview of the main mathematical tools used throughout the book. Requiring some familiarity with stochastic calculus methods, Continuous-Time Models in Corporate Finance will be useful for students, researchers, and professionals who want to develop dynamic models of firms' financial decisions.
| Author | : Robert J Elliott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 1475771460 |
This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.
| Author | : Michael U. Dothan |
| Publisher | : |
| Total Pages | : 368 |
| Release | : 1990 |
| Genre | : Business & Economics |
| ISBN | : |
This book offers a unified treatment of selected topics in the theory of financial markets. Starting with discrete time models, Dothan introduces discrete time stochastic calculus and discrete martingale methods of intuitive simplicity to characterize attainability, completeness, pricing, and the relationship between risk and return in financial markets. Subsequently, he uses the intuition developed in conjunction with the discrete time theory to introduce continuous time calculus for continuous, jump, and mixed continuous-jump processes, and to deal with attainability, completeness, pricing, and the relationship between risk and return in general continuous time models. Throughout, the exposition of the continuous time theory emphasizes the analogies between discrete time and continuous time methods and results. The book includes many examples, applications to the pricing of options and other derivative securities, and an extensive discussion of the Black-Scholes model and its most general theoretical extension.
| Author | : Robert A. Jarrow |
| Publisher | : Springer Nature |
| Total Pages | : 470 |
| Release | : 2021-07-30 |
| Genre | : Business & Economics |
| ISBN | : 3030744108 |
Asset pricing theory yields deep insights into crucial market phenomena such as stock market bubbles. Now in a newly revised and updated edition, this textbook guides the reader through this theory and its applications to markets. The new edition features new results on state dependent preferences, a characterization of market efficiency and a more general presentation of multiple-factor models using only the assumptions of no arbitrage and no dominance. Taking an innovative approach based on martingales, the book presents advanced techniques of mathematical finance in a business and economics context, covering a range of relevant topics such as derivatives pricing and hedging, systematic risk, portfolio optimization, market efficiency, and equilibrium pricing models. For applications to high dimensional statistics and machine learning, new multi-factor models are given. This new edition integrates suicide trading strategies into the understanding of asset price bubbles, greatly enriching the overall presentation and further strengthening the book’s underlying theme of economic bubbles. Written by a leading expert in risk management, Continuous-Time Asset Pricing Theory is the first textbook on asset pricing theory with a martingale approach. Based on the author’s extensive teaching and research experience on the topic, it is particularly well suited for graduate students in business and economics with a strong mathematical background.
| Author | : Jaksa Cvitanic |
| Publisher | : MIT Press |
| Total Pages | : 528 |
| Release | : 2004-02-27 |
| Genre | : Business & Economics |
| ISBN | : 9780262033206 |
An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models—a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.
| Author | : Jean-Luc Prigent |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 432 |
| Release | : 2013-03-14 |
| Genre | : Business & Economics |
| ISBN | : 3540248315 |
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
