Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 13.31
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Print on Demand. This book delves into the intricate world of financial models, examining the crucial concept of arbitrage and its impact on portfolio choice and option pricing. The author critically analyzes the development of continuous-time finance models, revealing how seemingly reasonable strategies like doubling strategies can lead to arbitrage profits and undermine the validity of theoretical results. The book then introduces the concept of a nonnegative wealth constraint, presenting a more economically sound approach to eliminating arbitrage opportunities. It explores the relationship between this constraint and the traditional integrability condition, demonstrating that the former is sufficient to preclude arbitrage while allowing for a broader range of feasible consumption plans. The author's rigorous analysis extends beyond the well-known Black-Scholes model, offering a more general framework for understanding the implications of nonnegative wealth in financial markets. This insightful book clarifies the theoretical complexities of arbitrage in continuous-time finance models, offering a valuable resource for researchers, students, and practitioners seeking a deeper understanding of these essential concepts. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781332975440_0
- Title
- Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans
- Author
- Philip H. Dybvig, Chi-Fu Huang
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332975445
- ISBN 13
- 9781332975440
- Seller catalogs
- Calculus
While much of the intuition in option pricing and portfolio choice can be exhibited in discrete time models, continuous time models using Ito calculus have been dominant in these areas of finance.l One reason is that it is generally easier to derive a closed  form solution to a differential equation than to a difference equation. Early development of continuous-time finance using Ito calculus tended to be intuitively based and assumed sufficiency of the natural first order conditions (see, for example, Merton [1971] and Black and Scholes The intuitive appeal of the results was reassuring, as was consistency with limiting versions of discrete-time results (as in Cox, Ross, and Rubinstein but at that time no attempt was made to make sure that the mathematical analysis was rigorously correct. Harrison and Kreps [1979] set out to give the continuous time analysis a rigorous foundation. They showed that this task is not straightforward, since arbitrage profits can be obtained using seemingly reasonable strategies called doubling strategies (after the strategy of doubling one's bet at roulette). Having continuous trading allows one to do in any finite time interval what would take infinitely many turns at the roulette wheel. Presence of the doubling strategies strikes at the core of the continuous time model, rendering it vacuous. Having arbitrage opportunities precludes having a solution to the optimal investment problem (for strictly monotone preferences) and, of course, invalidates option pricing theory based on the assumption that there is no arbitrage Opportunity. Harrison and Kreps removed arbitrage possibilities by restricting trading strategies to simple trading strategies that allow trade only at finitely many times chosen in advance. This restriction allowed them to use and formalize the risk  neutral pricing approach of Cox and Ross Cox and Ross argued that in the absence of arbitrage, one could always reassign the probabilities to give all assets the same expected returns. Harrison and Kreps called this approach the martingale approach because of its relation to martingale theory.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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