A Note On Mertons Optimum Consumption And Portfolio Rules In A Continuous Time Model PDF Download

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A Note on Merton's Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Revised

A Note on Merton's Optimum Consumption and Portfolio Rules in a Continuous-Time Model. Revised
Author: Suresh P. Sethi
Publisher:
Total Pages: 11
Release: 1986
Genre:
ISBN:

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In the area of consumption and portfolio problem in continuous time, Merton is the most widely cited paper. It is an important paper because of its many significant contributions. Among these was the provision of explicit solutions for utility functions in the HARA family specified in equation (43) of Merton's paper. These solutions in the form of lengthy formulas were simply stated without any derivation. Perhaps, because of this, some errors went undetected. While some minor errors were corrected in Merton, the purpose of this not is to delineate the subfamily of HARA utility functions for which the explicit solution obtained in Section 6 of Merton's paper are correct and the remaining subfamily for which they are not.


A Note on Robustness in Merton's Model of Intertemporal Consumption and Portfolio Choice

A Note on Robustness in Merton's Model of Intertemporal Consumption and Portfolio Choice
Author: Paolo Vanini
Publisher:
Total Pages:
Release: 2003
Genre:
ISBN:

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The paper presents a robust version of a simple two-assets Merton (1969, Review of Economics and Statistics 51, 247-57) model where the optimal choices and the implied shadow market prices of risk for a representative robust decision maker (RDM) can be easily described. With the exception of the log-utility case, precautionary behaviour is induced in the optimal consumption-investment rules through a substitution of investment in risky assets with both current consumption and riskless saving. For the log-utility case, precautionary behaviour arises only through a substitution between risky and riskless assets. On the financial side, the decomposition of the market price of risk in a standard consumption based component and a further price for model uncertainty risk (which is positively related to the robustness parameter) is independent of the underlying risk aversion parameter.


An Analytic Derivation of the Efficient Portfolio Frontier

An Analytic Derivation of the Efficient Portfolio Frontier
Author: Robert C. Merton
Publisher: Legare Street Press
Total Pages: 0
Release: 2022-10-27
Genre: History
ISBN: 9781016738392

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.


Applied Stochastic Control of Jump Diffusions

Applied Stochastic Control of Jump Diffusions
Author: Bernt Øksendal
Publisher: Springer Science & Business Media
Total Pages: 263
Release: 2007-04-26
Genre: Mathematics
ISBN: 3540698264

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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.


Robert C. Merton and the Science of Finance: A Collection

Robert C. Merton and the Science of Finance: A Collection
Author: Luis Garcia-Feijóo
Publisher: CFA Institute Research Foundation
Total Pages: 159
Release: 2020
Genre: Business & Economics
ISBN: 1944960074

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In 2019, MIT hosted a 75th birthday symposium in honor of Robert C. Merton. The event included presentations by students and colleagues explaining the influence Merton has had on the profession and on their ideas. Each presenter focused on a specific aspect of Merton’s life and contributions so that the audience could gain a full picture of Merton’s influence while avoiding repetition across presentations. The brief contains edited transcripts of some of the speeches and panel discussions that took place at the symposium. The presentations cover Merton’s career, highlighting both his foundational work on continuous time finance and the functional approach to understanding organizations as well as recent work on retirement security and trust. Some of the presentations unveil new aspects of his life. Merton’s father, Robert K. Merton, was one of the most important sociologists of the 20th century, being the originator of concepts such as role model, unanticipated consequences, and self-fulfilling prophecies. Another of the presentations makes a convincing case for Merton as the first financial engineer; the presenter argues that a body of knowledge becomes a science when a field of engineering emerges from it. If that is the case, this brief achieves two goals. It celebrates the influence of Merton on the theory and practice of finance through a series of engaging presentations, and it traces the birth of finance as a science on its own.


The Missing Billionaires

The Missing Billionaires
Author: Victor Haghani
Publisher: John Wiley & Sons
Total Pages: 423
Release: 2023-08-28
Genre: Business & Economics
ISBN: 1119747929

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An Economist Best Book of the Year "Making Money and Keeping It" – The Wall Street Journal Over the past century, if the wealthiest families had spent a reasonable fraction of their wealth, paid taxes, invested in the stock market, and passed their wealth down to the next generation, there would be tens of thousands of billionaire heirs to generations-old fortunes today. The puzzle of The Missing Billionaires is why you cannot find one such billionaire on any current rich list. There are a number of explanations, but this book is focused on one mistake which is of profound importance to all investors: poor risk decisions, both in investing and spending. Many of these families didn’t choose bad investments– they sized them incorrectly– and allowed their spending decisions to amplify this mistake. The Missing Billionaires book offers a simple yet powerful framework for making important lifetime financial decisions in a systematic and rational way. It's for readers with a baseline level of financial literacy, but doesn’t require a PhD. It fills the gap between personal finance books and the academic literature, bringing the valuable insights of academic finance to non-specialists. Part One builds the theory of optimal investment sizing from first principles, starting with betting on biased coins. Part Two covers lifetime financial decision-making, with emphasis on the integration of investment, saving and spending decisions. Part Three covers practical implementation details, including how to calibrate your personal level of risk-aversion, and how to estimate the expected return and risk on a broad spectrum of investments. The book is packed with case studies and anecdotes, including one about Victor’s investment with LTCM as a partner, and a bonus chapter on Liar’s Poker. The authors draw extensively on their own experiences as principals of Elm Wealth, a multi-billion-dollar wealth management practice, and prior to that on their years as arbitrage traders– Victor at Salomon Brothers and LTCM, and James at Nationsbank/CRT and Citadel. Whether you are young and building wealth, an entrepreneur invested heavily in your own business, or at a stage where your primary focus is investing and spending, The Missing Billionaires: A Guide to Better Financial Decisions is your must-have resource for thoughtful financial decision-making.


Hidden Markov Models in Finance

Hidden Markov Models in Finance
Author: Rogemar S. Mamon
Publisher: Springer Science & Business Media
Total Pages: 203
Release: 2007-04-26
Genre: Business & Economics
ISBN: 0387711635

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A number of methodologies have been employed to provide decision making solutions globalized markets. Hidden Markov Models in Finance offers the first systematic application of these methods to specialized financial problems: option pricing, credit risk modeling, volatility estimation and more. The book provides tools for sorting through turbulence, volatility, emotion, chaotic events – the random "noise" of financial markets – to analyze core components.


Optimal Consumption and Investment with Bankruptcy

Optimal Consumption and Investment with Bankruptcy
Author: Suresh P. Sethi
Publisher: Springer Science & Business Media
Total Pages: 434
Release: 2012-12-06
Genre: Business & Economics
ISBN: 1461562570

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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.


Stochastic Processes with Applications

Stochastic Processes with Applications
Author: Rabi N. Bhattacharya
Publisher: SIAM
Total Pages: 726
Release: 2009-08-27
Genre: Mathematics
ISBN: 0898716896

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This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes. The book features very broad coverage of the most applicable aspects of stochastic processes, including sufficient material for self-contained courses on random walks in one and multiple dimensions; Markov chains in discrete and continuous times, including birth-death processes; Brownian motion and diffusions; stochastic optimization; and stochastic differential equations. This book is for graduate students in mathematics, statistics, science and engineering, and it may also be used as a reference by professionals in diverse fields whose work involves the application of probability.


Methods of Mathematical Finance

Methods of Mathematical Finance
Author: Ioannis Karatzas
Publisher: Springer Science & Business Media
Total Pages: 427
Release: 1998-08-13
Genre: Business & Economics
ISBN: 0387948392

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This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion- driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options. Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8.