Download or read book Recursive Utility and Stochastic Differential Utility From Discrete to Continuous Time written by Thomas Seiferling and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 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 Forward Backward Stochastic Differential Equations and their Applications written by Jin Ma and published by Springer. This book was released on 2007-04-24 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

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 The Economics of Continuous Time Finance written by Bernard Dumas and published by MIT Press. This book was released on 2017-11-10 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advanced Asset Pricing Theory written by Ma Chenghu and published by World Scientific Publishing Company. This book was released on 2011-01-03 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction of modern asset pricing theory with equal treatments for both discrete-time and continuous-time modeling. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework.The analyses and coverage are up to date, comprehensive and in-depth. Topics include microeconomic foundation of asset pricing theory, the no-arbitrage principle and fundamental theorem, risk measurement and risk management, sequential portfolio choice, equity premium decomposition, option pricing, bond pricing and term structure of interest rates. The merits and limitations are expounded with respect to allocation and information market efficiency, along with the classical expectations hypothesis concerning the information content of yield curve and bond prices. Efforts are also made towards the resolution of several well-documented puzzles in empirical finance, which include the equity premium puzzle, the risk free rate puzzle, and the money-ness bias phenomenon of Black-Scholes option pricing model.The theory is self-contained and unified in presentation. The inclusion of proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory makes an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The explanations are detailed enough to capture the interest of those curious readers, and complete enough to provide necessary background material needed to explore further the subject and research literature.

Download or read book Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications written by Łukasz Delong and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Backward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.

Download or read book Convex Duality for Epstein Zin Stochastic Differential Utility written by Anis Matoussi and published by . This book was released on 2016 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and Epstein-Zin stochastic differential utility. Duality between the primal and dual problems is established. Consequently the optimal strategy of this consumption and investment problem is identified without assuming several technical conditions on market model, utility specification, and agent's admissible strategy. Meanwhile the minimizer of the dual problem is identified as the utility gradient of the primal value and is economically interpreted as the "least favorable" completion of the market.

Download or read book Ambiguity Risk and Asset Returns in Continuous Time written by Zengjing Chen and published by . This book was released on 2000 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Financial Asset Pricing Theory written by Claus Munk and published by Oxford University Press, USA. This book was released on 2013-04-18 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents models for the pricing of financial assets such as stocks, bonds, and options. The models are formulated and analyzed using concepts and techniques from mathematics and probability theory. It presents important classic models and some recent 'state-of-the-art' models that outperform the classics.

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 Economic Dynamics in Discrete Time written by Jianjun Miao and published by MIT Press. This book was released on 2014-09-19 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified, comprehensive, and up-to-date introduction to the analytical and numerical tools for solving dynamic economic problems. This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist's set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models. The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. The book goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the book's website. A solutions manual for students is available for sale from the MIT Press; a downloadable instructor's manual is available to qualified instructors.

Download or read book Optimal Consumption and Investment with Epstein Zin Recursive Utility written by Holger Kraft and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study continuous-time optimal consumption and investment with Epstein-Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton-Jacobi-Bellman equation by a fixed point argument and makes it possible to compute both indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.

Download or read book Consumption and Asset Prices with Recursive Preferences written by Mark Fisher and published by . This book was released on 1998 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book General Equilibrium Option Pricing Method Theoretical and Empirical Study written by Jian Chen and published by Springer. This book was released on 2018-04-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.