Download or read book Numerical Methods for an Optimal Investment consumption Model written by Ben George Fitzpatrick and published by . This book was released on 1989 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods in Finance written by L. C. G. Rogers and published by Cambridge University Press. This book was released on 1997-06-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
Download or read book Optimal Investment written by L. C. G. Rogers and published by Springer Science & Business Media. This book was released on 2013-01-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers of this book will learn how to solve a wide range of optimal investment problems arising in finance and economics. Starting from the fundamental Merton problem, many variants are presented and solved, often using numerical techniques that the book also covers. The final chapter assesses the relevance of many of the models in common use when applied to data.
Download or read book Handbook of Stochastic Analysis and Applications written by D. Kannan and published by CRC Press. This book was released on 2001-10-23 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Download or read book Optimal Consumption and Investment with Bankruptcy written by Suresh P. Sethi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers on continuous-time consumption investment models by Suresh Sethi and various co-authors. Sir Isaac Newton said that he saw so far because he stood on the shoulders of gi ants. Giants upon whose shoulders Professor Sethi and colleagues stand are Robert Merton, particularly Merton's (1969, 1971, 1973) seminal papers, and Paul Samuelson, particularly Samuelson (1969). Karatzas, Lehoczky, Sethi and Shreve (1986), henceforth KLSS, re produced here as Chapter 2, reexamine the model proposed by Mer ton. KLSS use methods of modern mathematical analysis, taking care to prove the existence of integrals, check the existence and (where appro priate) the uniqueness of solutions to equations, etc. KLSS find that un der some conditions Merton's solution is correct; under others, it is not. In particular, Merton's solution for aHARA utility-of-consumption is correct for some parameter values and not for others. The problem with Merton's solution is that it sometimes violates the constraints against negative wealth and negative consumption stated in Merton (1969) and presumably applicable in Merton (1971 and 1973). This not only affects the solution at the zero-wealth, zero-consumption boundaries, but else where as well. Problems with Merton's solution are analyzed in Sethi and Taksar (1992), reproduced here as Chapter 3.
Download or read book Optimal Investment Planning written by R. K. Das and published by Gower Publishing Company, Limited. This book was released on 1974 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monograph introducing a model to illustrate investment policy and resource allocation choices for India in the context of optimal economic planning - covers wages constraints on economic growth, strategies for growth with income redistribution, strategies for capital investment and capital goods accumulation, etc. Bibliography pp. 143 to 146 and graphs.
Download or read book Numerical Analysis of a Free Boundary Singular Control Problem in Financial Economics written by Ayman Hindy and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze a numerical scheme for solving the consumption and investment allocation problem studied in a companion paper by Hindy, Huang, and Zhu (1993). For this problem, Bellman's equation is a differential inequality involving second order partial differential equation with gradient constraints. The solution involves finding a free-boundary at which consumption occurs. We prove that the value function is the unique viscosity solution to Bellman's equation. We describe a numerical analysis technique based on Markov chain approximation schemes. We approximate the original continuous time problem by a sequence of discrete parameter Markov chains control problems. We prove that the value functions and the optimal investment policies in the sequence of the approximating control problems converge to the value function and the optimal investment policy, if it exists, of the original problem. We also show that the optimal consumption and abstinence regions in the sequence of approximating problems converge to those in the original problem.
Download or read book Optimal Consumption and Portfolio Rules with Durability and Habit Formation written by Ayman Hindy and published by . This book was released on 1993 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Modelling and Numerical Methods in Finance written by Alain Bensoussan and published by Elsevier. This book was released on 2009-06-16 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas and results Contributors are leaders of the field
Download or read book Introduction to Mathematical Finance written by David C. Heath Glen Swindle and published by American Mathematical Soc.. This book was released on 2000-01-25 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Theorie de la speculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought remarkable and important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and growth. Concurrently with these mathematical advances, markets have grown, and developments in both academia and industry continue to expand. This lively activity inspired an AMS Short Course at the Joint Mathematics Meetings in San Diego (CA). The present volume includes the written results of that course. Articles are featured by an impressive list of recognized researchers and practitioners. Their contributions present deep results, pose challenging questions, and suggest directions for future research. This collection offers compelling introductory articles on this new, exciting, and rapidly growing field.
Download or read book An Approximation Algorithm for Optimal Consumption Investment Problems written by Sanjiv Ranjan Das and published by . This book was released on 2009 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article develops a simple approach to solving continuous-time portfolio choice problems. Portfolio problems for which no closed-form solutions are available may be handled by this technique, which substitutes the numerical solution of partial differential equations with a non-linear numerical algorithm approximating the solution. This paper complements the wide literature in economics on the solution of dynamic problems in dicrete time. The algorithm is parismonious, and is illustrated by solving two examples, one, the standard Merton problem, and two, a jump-diffusion problem.
Download or read book Optimal Investment consumption Models with Constraints written by Thaleia Zariphopoulou and published by . This book was released on 1989 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Stochastic Models and Control for Finance and Insurance written by Charles S. Tapiero and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Stochastic Models and Control for Finance and Insurance presents at an introductory level some essential stochastic models applied in economics, finance and insurance. Markov chains, random walks, stochastic differential equations and other stochastic processes are used throughout the book and systematically applied to economic and financial applications. In addition, a dynamic programming framework is used to deal with some basic optimization problems. The book begins by introducing problems of economics, finance and insurance which involve time, uncertainty and risk. A number of cases are treated in detail, spanning risk management, volatility, memory, the time structure of preferences, interest rates and yields, etc. The second and third chapters provide an introduction to stochastic models and their application. Stochastic differential equations and stochastic calculus are presented in an intuitive manner, and numerous applications and exercises are used to facilitate their understanding and their use in Chapter 3. A number of other processes which are increasingly used in finance and insurance are introduced in Chapter 4. In the fifth chapter, ARCH and GARCH models are presented and their application to modeling volatility is emphasized. An outline of decision-making procedures is presented in Chapter 6. Furthermore, we also introduce the essentials of stochastic dynamic programming and control, and provide first steps for the student who seeks to apply these techniques. Finally, in Chapter 7, numerical techniques and approximations to stochastic processes are examined. This book can be used in business, economics, financial engineering and decision sciences schools for second year Master's students, as well as in a number of courses widely given in departments of statistics, systems and decision sciences.
Download or read book RAIRO written by and published by . This book was released on 2009 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Optimal Investment consumption Model with Borrowing written by Wendell Helms Fleming and published by . This book was released on 1989 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimal Consumption and Portfolio Allocation Under Mean Reverting Returns written by Jessica A. Wachter and published by . This book was released on 2011 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and the behavior of approximate log-linear solutions. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time.
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.
