Optimal Portfolios Stochastic Models For Optimal Investment And Risk Management In Continuous Time
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| Author | : Ralf Korn |
| Publisher | : World Scientific |
| Total Pages | : 352 |
| Release | : 1997 |
| Genre | : Business & Economics |
| ISBN | : 9812385347 |
The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.
| Author | : Ralf Korn |
| Publisher | : World Scientific |
| Total Pages | : 352 |
| Release | : 1997-11-29 |
| Genre | : Business & Economics |
| ISBN | : 9814497126 |
The focus of the book is the construction of optimal investment strategies in a security market model where the prices follow diffusion processes. It begins by presenting the complete Black-Scholes type model and then moves on to incomplete models and models including constraints and transaction costs. The models and methods presented will include the stochastic control method of Merton, the martingale method of Cox-Huang and Karatzas et al., the log optimal method of Cover and Jamshidian, the value-preserving model of Hellwig etc.Stress is laid on rigorous mathematical presentation and clear economic interpretations while technicalities are kept to the minimum. The underlying mathematical concepts will be provided. No a priori knowledge of stochastic calculus, stochastic control or partial differential equations is necessary (however some knowledge in stochastics and calculus is needed).
| Author | : Holger Kraft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 190 |
| Release | : 2004-04-13 |
| Genre | : Business & Economics |
| ISBN | : 9783540212300 |
The continuous-time portfolio problem consists of finding the optimal investment strategy of an investor. In the classical Merton problem the investor can allocate his funds to a riskless savings account and risky assets. However, to get explicit results, it is assumed that the interest rates are deterministic and that the assets are default free. In this monograph both assumptions are weakened: The author analyzes and solves portfolio problems with stochastic interest rates and with defaultable assets. Besides, he briefly discusses how portfolio problems with foreign assets can be handled. The focus of the monograph is twofold: On the one hand, the economical problems are carefully explained, on the other hand their formal solution is rigorously presented. For this reason the text should be of interest to researchers with a Finance background as well as to researchers with a more formal background who would like to see how mathematics is applied to portfolio theory. TOC:Preliminaries from Stochastics.- Optimal Portfolios with Stochastic Interest Rates.- Elasticity Approach to Portfolio Optimization.- Barrier Derivatives with Curved Boundaries.- Optimal Portfolios with Dafaultable Assets - A Firm Value Approach.- References.- Abbreviations.- Notations.
| Author | : W. T. Ziemba |
| Publisher | : World Scientific |
| Total Pages | : 756 |
| Release | : 2006 |
| Genre | : Business & Economics |
| ISBN | : 9812773657 |
A reprint of one of the classic volumes on portfolio theory and investment, this book has been used by the leading professors at universities such as Stanford, Berkeley, and Carnegie-Mellon. It contains five parts, each with a review of the literature and about 150 pages of computational and review exercises and further in-depth, challenging problems. Frequently referenced and highly usable, the material remains as fresh and relevant for a portfolio theory course as ever. Sample Chapter(s). Chapter 1: Expected Utility Theory (373 KB). Contents: Mathematical Tools: Expected Utility Theory; Convexity and the Kuhn-Tucker Conditions; Dynamic Programming; Qualitative Economic Results: Stochastic Dominance; Measures of Risk Aversion; Separation Theorems; Static Portfolio Selection Models: Mean-Variance and Safety First Approaches and Their Extensions; Existence and Diversification of Optimal Portfolio Policies: Effects of Taxes on Risk Taking; Dynamic Models Reducible to Static Models: Models That Have a Single Decision Point; Risk Aversion over Time Implies Static Risk Aversion; Myopic Portfolio Policies; Dynamic Models: Two-Period Consumption Models and Portfolio Revision; Models of Optimal Capital Accumulation and Portfolio Selection; Models of Option Strategy; The Capital Growth Criterion and Continuous-Time Models. Readership: Postdoctoral and graduate students, researchers, academics, and professionals interested in portfolio theory and stochastic optimization.
| Author | : Siddhartha Pratim Chakrabarty |
| Publisher | : Springer Nature |
| Total Pages | : 158 |
| Release | : 2023-02-18 |
| Genre | : Mathematics |
| ISBN | : 9811985448 |
Designed as a self-contained text, this book covers a wide spectrum of topics on portfolio theory. It covers both the classical-mean-variance portfolio theory as well as non-mean-variance portfolio theory. The book covers topics such as optimal portfolio strategies, bond portfolio optimization and risk management of portfolios. In order to ensure that the book is self-contained and not dependent on any pre-requisites, the book includes three chapters on basics of financial markets, probability theory and asset pricing models, which have resulted in a holistic narrative of the topic. Retaining the spirit of the classical works of stalwarts like Markowitz, Black, Sharpe, etc., this book includes various other aspects of portfolio theory, such as discrete and continuous time optimal portfolios, bond portfolios and risk management. The increase in volume and diversity of banking activities has resulted in a concurrent enhanced importance of portfolio theory, both in terms of management perspective (including risk management) and the resulting mathematical sophistication required. Most books on portfolio theory are written either from the management perspective, or are aimed at advanced graduate students and academicians. This book bridges the gap between these two levels of learning. With many useful solved examples and exercises with solutions as well as a rigorous mathematical approach of portfolio theory, the book is useful to undergraduate students of mathematical finance, business and financial management.
| Author | : Bernt Øksendal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2007-04-26 |
| Genre | : Mathematics |
| ISBN | : 3540698264 |
Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
| Author | : Joachim Rosenthal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 0387216960 |
This volume contains survey and research articles by some of the leading researchers in mathematical systems theory - a vibrant research area in its own right. Many authors have taken special care that their articles are self-contained and accessible also to non-specialists.
| Author | : Ulrich Derigs |
| Publisher | : EOLSS Publications |
| Total Pages | : 460 |
| Release | : 2009-04-15 |
| Genre | : |
| ISBN | : 1905839510 |
Optimization and Operations Research is a component of Encyclopedia of Mathematical Sciences in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme on Optimization and Operations Research is organized into six different topics which represent the main scientific areas of the theme: 1. Fundamentals of Operations Research; 2. Advanced Deterministic Operations Research; 3. Optimization in Infinite Dimensions; 4. Game Theory; 5. Stochastic Operations Research; 6. Decision Analysis, which are then expanded into multiple subtopics, each as a chapter. These four volumes are aimed at the following five major target audiences: University and College students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers and NGOs.
| Author | : Stavros A. Zenios |
| Publisher | : Elsevier |
| Total Pages | : 685 |
| Release | : 2007-08-08 |
| Genre | : Business & Economics |
| ISBN | : 0080548563 |
The Handbooks in Finance are intended to be a definitive source for comprehensive and accessible information in the field of finance. Each individual volume in the series presents an accurate self-contained survey of a sub-field of finance, suitable for use by finance and economics professors and lecturers, professional researchers, graduate students and as a teaching supplement. It is fitting that the series Handbooks in Finance devotes a handbook to Asset and Liability Management. Volume 2 focuses on applications and case studies in asset and liability management.The growth in knowledge about practical asset and liability modeling has followed the popularity of these models in diverse business settings. This volume portrays ALM in practice, in contrast to Volume 1, which addresses the theories and methodologies behind these models. In original articles practitioners and scholars describe and analyze models used in banking, insurance, money management, individual investor financial planning, pension funds, and social security. They put the traditional purpose of ALM, to control interest rate and liquidity risks, into rich and broad-minded frameworks. Readers interested in other business settings will find their discussions of financial institutions both instructive and revealing.* Focuses on pragmatic applications * Relevant to a variety of risk-management industries* Analyzes models used in most financial sectors
| Author | : Carles Casacuberta |
| Publisher | : Birkhäuser |
| Total Pages | : 630 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034882661 |
This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.
