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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: In this paper, the authors exploit the restrictions of intertemporal portfolio choice in the presence of non-nancial income risk to design and implement tests of hedging that use the information contained in the actual portfolio of the investor.
Abstract: We exploit the restrictions of intertemporal portfolio choice in the presence of nonÞnancial income risk to design and implement tests of hedging that use the information contained in the actual portfolio of the investor. We use a unique dataset of Swedish investors with information broken down at the investor level and into various components of wealth, investor income, tax positions and investor demographic characteristics. Portfolio holdings are identiÞed at the stock level. We show that investors do not engage in hedging, but invest in stocks closely related to their non-Þnancial income. We explain this with familiarity, that is the tendency to concentrate holdings in stocks with which the investor is familiar in terms of geographical or professional proximity or that he has held for a long period. We show that familiarity is not a behavioral bias, but is information-driven. Familiarity-based investment allows investors to earn higher returns than they would have otherwise earned if they had hedged.

457 citations

Journal ArticleDOI
TL;DR: In this article, a stationary portfolio policy is proposed, in which portfolio proportions are allowed to fluctuate with portfolio consumption, in the form of two control barriers between portfolio proportions, and the expected utility is maximized.
Abstract: The presence of any friction in financial markets qualitatively changes the nature of the optimization problem faced by an investor. It requires one to either act or do nothing, an issue which, of course, does not arise in frictionless situations. The investor considered here accumulates wealth without consuming until some terminal point in time when he consumes all. His objective is to maximize the expected utility derived from that terminal consumption. We postpone the terminal point far into the future to obtain a stationary portfolio rule. The portfolio policy is in the form of two control barriers between which portfolio proportions are allowed to fluctuate. We show how to calculate them.

445 citations

Journal ArticleDOI
TL;DR: In this article, the authors provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models.
Abstract: Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman differential equation. A calibration exercise shows that the mean-variance hedging demands may comprise a significant fraction of the investor's total risky asset demand.

443 citations

Journal ArticleDOI
TL;DR: The authors study portfolio choice when labor income and dividends are cointegrated, and find that young investors should take substantial short positions in the stock market and their human capital becomes more stock-like.
Abstract: We study portfolio choice when labor income and dividends are cointegrated. Economically plausible calibrations suggest young investors should take substantial short positions in the stock market. Because of cointegration the young agent’s human capital efiectively becomes \stock-like." However, for older agents with shorter times-to-retirement, cointegration does not have su‐cient time to act, and thus their human capital becomes more \bond-like." Together, these efiects create hump-shaped life-cycle portfolio holdings, consistent with empirical observation. These results hold even when asset return predictability is accounted for.

443 citations


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

  • ...For instance, Merton (1971), Svensson and Werner (1993), and Koo (1998) study portfolio choice in the presence of nontraded labor income....

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Journal ArticleDOI
TL;DR: In this paper, an approximate solution method for the optimal consumption and portfolio choice problem of an infinitely long-lived investor with Epstein-Zin utility was developed for a set of asset returns described by a vector autoregression in returns and state variables.

436 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