Optimal Investment

verfasst von: L. C. G. Rogers

Verlag: Springer Berlin Heidelberg

Buchreihe : SpringerBriefs in Quantitative Finance

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. The Merton Problem

Abstract

The first chapter of the book introduces the classical Merton problems of optimal investment over a finite horizon to maximize expected utility of terminal wealth; and of optimal investment over an infinite horizon to maximize expected integrated utility of running consumption. The workhorse method is to find the Hamilton-Jacobi-Bellman equations for the value function and then to try to solve these in some way. However, in a complete market we can often use the budget constraint as the necessary and sufficient restriction on possible consumption streams to arrive quickly at optimal solutions. The third main method is to use the Pontryagin-Lagrange approach, which is an example of dual methods.

L. C. G. Rogers

Chapter 2. Variations

Abstract

The second chapter of the book studies a wide range of different examples which are all in some sense variations on the basic Merton examples of Chapter 1. We study what happens when preferences change; or asset dynamics are changed; or objectives are changed.

L. C. G. Rogers

Chapter 3. Numerical Solution

Abstract

The third chapter of the book presents the main numerical methods that are useful in calculating solutions to the optimal control problems of earlier chapters when analytic methods fail. The main technique is policy improvement, but this requires an effective translation of an optimization problem for a controlled diffusion into an optimization problem for a controlled Markov chain, and various techniques for this are discussed.

L. C. G. Rogers

Chapter 4. How Well Does It Work?

Abstract

The final chapter of the book takes a look at data, and finds virtually all of the models of the earlier part of the book to be wanting. Stylized facts of return data, well known to econometricians, are surprisingly robust across asset classes, and do not sit comfortably with the assumptions made in most of the theoretical literature.

L. C. G. Rogers

Backmatter

Titel: Optimal Investment
verfasst von: L. C. G. Rogers
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-35202-7
Print ISBN: 978-3-642-35201-0
DOI: https://doi.org/10.1007/978-3-642-35202-7