Download or read book Recursive Utility Using the Stochastic Maximum Principle written by Knut K. Aase and published by . This book was released on 2015 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the problems of the conventional model in rationalizing market data, we derive the equilibrium interest rate and risk premiums using recursive utility in a continuous time model. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. With existence granted, the market portfolio is determined in terms of future utility and aggregate consumption in equilibrium. The equilibrium real interest rate is also derived, and the the model is shown to be consistent with reasonable values of the parameters of the utility function when calibrated to market data, under various assumptions.

Download or read book Recursive Utility and Jump Diffusions written by Knut K. Aase and published by . This book was released on 2015 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive the equilibrium interest rate and risk premiums using recursive utility for jump-diffusions. Compared to to the continuous version, including jumps allows for a separate risk aversion related to jump size risk in addition to risk aversion related to the continuous part. The jump part also introduces moments of higher orders that may matter in many circumstances. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. We demonstrate how the stochastic process for the market portfolio is determined in terms the corresponding processes for future utility and aggregate consumption. It is indicated that this model has the potential to give reasonable explanations of empirical puzzles.

Download or read book Efficient Intertemporal Allocations with Recursive Utility written by Bernard Dumas and published by . This book was released on 1999 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, our objective is to determine efficient allocations in economies with multiple agents having recursive utility functions. Our main result is to show that in a multiagent economy, the problem of determining efficient allocations can be characterized in terms of a single value function (that of a social planner), rather than multiple functions (one for each investor), as has been proposed thus far (Duffie, Geoffard and Skiadas (1994)). We then show how the single value function can be identified using the familiar technique of stochastic dynamic programming. We achieve these goals by first extending to a stochastic environment Geoffard's (1996) concept of variational utility and his result that variational utility is equivalent to recursive utility, and then using these results to characterize allocations in a multiagent setting.

Download or read book Stochastic Controls written by Jiongmin Yong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation.

Download or read book Control of Distributed Parameter and Stochastic Systems written by Shuping Chen and published by Springer. This book was released on 2013-06-05 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical treatment of many problems which arise in physics, economics, engineering, management, etc., the researcher frequently faces two major difficulties: infinite dimensionality and randomness of the evolution process. Infinite dimensionality occurs when the evolution in time of a process is accompanied by a space-like dependence; for example, spatial distribution of the temperature for a heat-conductor, spatial dependence of the time-varying displacement of a membrane subject to external forces, etc. Randomness is intrinsic to the mathematical formulation of many phenomena, such as fluctuation in the stock market, or noise in communication networks. Control theory of distributed parameter systems and stochastic systems focuses on physical phenomena which are governed by partial differential equations, delay-differential equations, integral differential equations, etc., and stochastic differential equations of various types. This has been a fertile field of research with over 40 years of history, which continues to be very active under the thrust of new emerging applications. Among the subjects covered are: Control of distributed parameter systems; Stochastic control; Applications in finance/insurance/manufacturing; Adapted control; Numerical approximation . It is essential reading for applied mathematicians, control theorists, economic/financial analysts and engineers.

Download or read book An Introduction to Optimal Control of FBSDE with Incomplete Information written by Guangchen Wang and published by Springer. This book was released on 2018-05-16 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. ​Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.

Download or read book Stochastic Differential Utility as the Continuous time Limit of Recursive Utility written by Holger Kraft and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size.

Download or read book Stochastic Analysis and Applications written by Fred Espen Benth and published by Springer Science & Business Media. This book was released on 2007-04-24 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over presented the newest developments within the exciting and fast growing field of stochastic analysis. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion.

Download or read book Stochastics of Environmental and Financial Economics written by Fred Espen Benth and published by Springer. This book was released on 2015-10-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Proceedings offer a selection of peer-reviewed research and survey papers by some of the foremost international researchers in the fields of finance, energy, stochastics and risk, who present their latest findings on topical problems. The papers cover the areas of stochastic modeling in energy and financial markets; risk management with environmental factors from a stochastic control perspective; and valuation and hedging of derivatives in markets dominated by renewables, all of which further develop the theory of stochastic analysis and mathematical finance. The papers were presented at the first conference on “Stochastics of Environmental and Financial Economics (SEFE)”, being part of the activity in the SEFE research group of the Centre of Advanced Study (CAS) at the Academy of Sciences in Oslo, Norway during the 2014/2015 academic year.

Download or read book Foundations of Continuous time Recursive Utility Differentiability and Normalization of Certainty Equivalents written by Holger Kraft and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Optimization in Continuous Time written by Fwu-Ranq Chang and published by Cambridge University Press. This book was released on 2004-04-26 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.

Download or read book Applied Stochastic Control of Jump Diffusions written by Bernt Øksendal and published by Springer. This book was released on 2019-04-17 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Real Options Ambiguity Risk and Insurance written by A. Bensoussan and published by IOS Press. This book was released on 2013-05-02 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial engineering has become the focus of widespread media attention as a result of the worldwide financial crisis of recent years. This book is the second in a series dealing with financial engineering from Ajou University in Korea. The main objective of the series is to disseminate recent developments and important issues in financial engineering to graduate students and researchers, and to provide surveys or pedagogical exposition of important published papers in a broad perspective, as well as analyses of important financial news concerning financial engineering research, practices or regulations. Real Options, Ambiguity, Risk and Insurance, comprises 12 chapters and is divided into three parts. In Part I, five chapters deal with real options analysis, which addresses the issue of investment decisions in complex, innovative or risky projects. Part II presents three chapters on ambiguity. The notion of ambiguity is one of the major breakthroughs in the expected utility theory; ambiguity arises as uncertainties cannot be precisely described in the probability space. Part III consists of four chapters devoted to risk and insurance, and covers mutual insurance for non-traded risks, downside risk management, and credit risk in fixed income markets. This volume will be useful to both graduate students and researchers in understanding relatively new areas in economics and finance, as well as challenging aspects of mathematics.

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü and published by Springer Nature. This book was released on 2021-10-19 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Download or read book Seminar on Stochastic Analysis Random Fields and Applications IV written by Robert Dalang and published by Birkhäuser. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains twenty refereed papers presented at the 4th Seminar on Stochastic Processes, Random Fields and Applications, which took place in Ascona, Switzerland, from May 2002. The seminar focused mainly on stochastic partial differential equations, stochastic models in mathematical physics, and financial engineering. The book will be a valuable resource for researchers in stochastic analysis and professionals interested in stochastic methods in finance and insurance.

Download or read book Issues in Systems Engineering 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Systems Engineering / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Systems and Control Engineering. The editors have built Issues in Systems Engineering: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Systems and Control Engineering in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Systems Engineering: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book The Equity Premium in a Production Economy A New Perspective Involving Recursive Utility written by Knut K. Aase and published by . This book was released on 2015 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a rational expectations' competitive equilibrium in a production economy, i.e., a system of prices at which firms' profit maximizing production decisions and individuals' preferred affordable consumption choices equate supply and demand in every market. We derive the equilibrium price of the firm and the equilibrium short term interest rate, the optimal per capita consumption in society, as well as the risk premium on equity. First a simple linear production technology with constant coefficients is studied, then a more general technology, and finally a general production economy with recursive utility is analyzed by the use of the stochastic maximum principle. While the two first models can not explain the empirics well using conventional preferences, the latter model is found to be much more promising in this regard. We also demonstrate a simple proof for the ICAPM.