Optimum consumption and portfolio rules in a continuous-time model☆
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.
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TL;DR: In this paper, the authors solve for optimal portfolios when interest rates and labor income are stochastic with the expected income growth being affine in the short-term interest rate in order to encompass business cycle variations in wages.
104 citations
TL;DR: In this paper, the authors study the movements in equity prices caused by variation over time in uncertainty about corporate dividends and find that risk premiums on levered equity are a monotonically increasing function of junk bond yield spreads.
104 citations
TL;DR: In this article, the authors estimate a conditional CAPM with time-varying betas and find that the post-1963 book-to-market effect is statistically insignificant, while the momentum effect is robust to small sample biases, the reversal effect is not.
Abstract: Over the long-run from 1926 to 2001, the CAPM can account for the spread in the returns of portfolios sorted by book-to-market ratios. In contrast, using data covering the period after 1963, many studies find strong evidence of a book-to-market effect using conventional asymptotic standard errors. To conduct correct small sample inference, we estimate a conditional CAPM with time-varying betas and find that post-1963 book-to-market effect is statistically insignificant. We find some evidence of a book-to-market effect among medium-sized stocks, but not among the smallest stocks. We also find that while the momentum effect is robust to small sample biases, the reversal effect is not.
104 citations
TL;DR: In this article, the optimal portfolio policy of a HARA-utility investor is derived explicitly using standard option pricing results, which is shown to be equivalent to the investor's optimal unconstrained policy when he has contracted to paying out a proportion of the value of the benchmark portfolio at the terminal date.
104 citations
TL;DR: In this paper, the authors examined the optimal production of a resource such as oil when its price is determined exogenously (e.g. by a cartel such as OPEC), and is subject to stochastic fluctuations away from an expected growth path.
Abstract: This paper examines the optimal production of a resource such as oil when its price is determined exogenously (e.g. by a cartel such as OPEC), and is subject to stochastic fluctuations away from an expected growth path. We first examine the dependence of production on extraction cost, and show that the conventional exponential decline curve is indeed optimal if marginal cost is constant with respect to the rate of extraction but is a hyperbolic function of the reserve level. We next show that uncertainty about future price affects the optimal production rate in two ways. First, if marginal cost is a convex (concave) function of the rate of production, stochastic fluctuations in price raise (lower) average cost over time, so that there is an incentive to speed up (slow down) production. Second, the “option” value of the reserve, i.e. the ability to withhold production indefinitely and never incur the cost of extraction, provides an incentive to slow down the rate of production.
104 citations
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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
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
987 citations