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Journal ArticleDOI

Optimum consumption and portfolio rules in a continuous-time model☆

01 Dec 1971-Journal of Economic Theory (Academic Press)-Vol. 3, Iss: 4, pp 373-413
TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
About: This article is published in Journal of Economic Theory.The article was published on 1971-12-01 and is currently open access. It has received 4952 citations till now. The article focuses on the topics: Geometric Brownian motion & Intertemporal portfolio choice.
Citations
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Book
08 Sep 2011
TL;DR: In this paper, the authors use stochastic dynamic programming to study the intertemporal consumption and portfolio choice of an infinitely lived agent who faces a constant opportunity set and a borrowing constraint.
Abstract: In this paper, we use stochastic dynamic programming to study the intertemporal consumption and portfolio choice of an infinitely lived agent who faces a constant opportunity set and a borrowing constraint. We show that, under general assumptions on the agent's utility function, optimal policies exist and can be expressed as feedback functions of current wealth. We describe these policies in detail, when the agent's utility function exhibits constant relative risk aversion.Journal of Economic LiteratureClassification Numbers: G11, G12, D52.

78 citations

Journal ArticleDOI
TL;DR: In this article, the boundary behavior and optimal portfolio rules for cases when marginal utility at zero consumption is finite are discussed. But they do not satisfy the Hamilton-Jacobi Bellman equations and do not represent appropriate value functions because the boundary behaviour near zero wealth is not satisfactorily dealt with.

78 citations

Journal ArticleDOI
Klaus Wälde1
TL;DR: In this paper, the optimal saving and investment behavior of a household that can either invest in a riskless or a risky saving technology when risk results from a Poisson process is studied.

77 citations


Cites methods from "Optimum consumption and portfolio r..."

  • ...Despite the popularity of Poisson-based models, only Merton [ 11 ] has studied optimal saving decisions of a risk-averse household when the household’s budget constraint contains some Poisson distributed stochastic variables....

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Book ChapterDOI
TL;DR: In this paper, the state-of-the-art of heterogeneous agent models (HAMs) in finance using a jointly theoretical and empirical analysis, combined with numerical analysis from the latest development in computational finance is surveyed.
Abstract: This chapter surveys the state-of-art of heterogeneous agent models (HAMs) in finance using a jointly theoretical and empirical analysis, combined with numerical analysis from the latest development in computational finance. It provides supporting evidence on the explanatory power of HAMs to various stylized facts and market anomalies through model calibration, estimation, and economic mechanisms analysis. It presents HAMs with the mainstream finance a unified framework in continuous time to study the impact of historical price information on price dynamics, profitability and optimality of fundamental and momentum trading. It demonstrates how HAMs can help to understand stock price co-movements and evolutionary CAPM. It also introduces a new HAMs perspective on house price dynamics and an integrate approach to study dynamics of limit order markets. The survey provides further insights into the complexity and efficiency of financial markets and policy implications.

77 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present a model which shows that the currency composition of a country's external debt can serve as a hedging instrument against changes in exchange rates and commodity prices.

77 citations

References
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Journal ArticleDOI
TL;DR: In this paper, the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model was examined, where his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic.
Abstract: OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.

4,908 citations

Book
01 Jan 1965
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
Abstract: This book should be of interest to undergraduate and postgraduate students of probability theory.

3,597 citations

Book ChapterDOI
TL;DR: In this paper, the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions), is discussed.
Abstract: Publisher Summary This chapter reviews the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions). It presents a generalization of Phelps' model to include portfolio choice and consumption. The explicit form of the optimal solution is derived for the special case of utility functions having constant relative risk aversion. The optimal portfolio decision is independent of time, wealth, and the consumption decision at each stage. Most analyses of portfolio selection, whether they are of the Markowitz–Tobin mean-variance or of more general type, maximize over one period. The chapter only discusses special and easy cases that suffice to illustrate the general principles involved and presents the lifetime model that reveals that investing for many periods does not itself introduce extra tolerance for riskiness at early or any stages of life.

2,369 citations

Book
17 Jan 2012
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
Abstract: Book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes

1,293 citations