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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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Journal ArticleDOI
TL;DR: The authors construct a world equilibrium model in which productivity varies across countries and international borrowing and lending take place to exploit good investment opportunities, and the model generates the novel prediction that favorable income shocks lead to current account deficits in debtor countries and current account surpluses in creditor countries.
Abstract: The authors reexamine a classic question in international economics: What is the current account response to a transitory income shock such as a temporary improvement in the terms of trade, a transfer from abroad, or unusually high production? To answer this question, they construct a world equilibrium model in which productivity varies across countries and international borrowing and lending take place to exploit good investment opportunities. Despite its conventional ingredients, the model generates the novel prediction that favorable income shocks lead to current account deficits in debtor countries and current account surpluses in creditor countries. Evidence from thirteen OECD countries broadly supports this theoretical prediction.

161 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide the solution to an inter-temporal investment problem where the investor has power utility and can invest in stocks and bonds in a complete market setting where the Vasicek term structure model applies.
Abstract: This paper provides the solution to an intertemporal investment problem. The investor has power utility and can invest in stocks and bonds in a complete market setting where the Vasicek term structure model applies. The paper demonstrates that the zero-coupon bond with maturity at the investment horizon is the appropriate instrument for hedging changes in the opportunity set. Implementation issues are discussed and it is shown how the intertemporal investment problem can be recast as a series of mean-variance problems in terms of drift and volatility of the wealth forward price. An application based on a quasi-dynamic programming approach is considered.

160 citations


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

  • ...The portfolio choice is, in general, described by two terms: a speculative term and a hedging term as originally described by Merton (1971). The first term on the right-hand side of (7) is the speculative term, which describes how the portfolio choice depends on the expected excess return on the available securities....

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  • ..., Merton (1993))....

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Journal ArticleDOI
TL;DR: This paper used an intertemporal mean-variance model of the market for a dividend-paying risky asset to analyse rational expectations equilibria when all agents condition their expectations on past rather than current prices.

159 citations

Journal ArticleDOI
TL;DR: This article showed that trade costs in goods markets do not explain the consumption and portfolio home biases in a two-country/two-good stochastic equilibrium model with trade costs, and that the trade costs create a foreign bias in portfolios for reasonable parameter values.

159 citations

Journal ArticleDOI
TL;DR: In this paper, the authors solve the portfolio problem of a long-run investor when the term structure is Gaussian and when the investor has access to nominal bonds and stock and apply their method to a three-factor model that captures the failure of the expectations hypothesis.
Abstract: We solve the portfolio problem of a long-run investor when the term structure is Gaussian and when the investor has access to nominal bonds and stock We apply our method to a three-factor model that captures the failure of the expectations hypothesis We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data The estimates imply that the bond portfolio of a long-run investor looks very different from the portfolio of a meanvariance optimizer In particular, time-varying term premia generate large hedging demands for long-term bonds

158 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