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 article, the authors present closed-form solutions for a large class of stochastic general equilibrium models, some of which have undesirable features, such as undesirable features such as non-triviality and non-convexity.
Abstract: Properties of dynamic stochastic general equilibrium models can be revealed by either using numerical solutions or qualitative analysis. Very precise and intuition-building results are obtained by working with models which provide closed-form solutions. Closed-form solutions are known for a large class of models some of which, however, have some undesirable features. This paper offers closed-form solutions for models which are just as tractable but do not suffer from these shortcomings.
94 citations
Cites background from "Optimum consumption and portfolio r..."
...The seminal papers are the finance papers by Merton (1969, 1971) and his (1975) Solow growth model with stochastic population growth....
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TL;DR: In this paper, the authors extended the analysis of asset pricing when information is incomplete by relaxing some of the restrictive assumptions of the Gaussian model studied earlier in the literature, and used a separation theorem to produce a closed-form solution for the interest rate process when the investor's utility function is logarithmic.
94 citations
TL;DR: In this paper, the authors present a new approach for analyzing dynamic investment strategies, which is called the inverse problem: given any specific dynamic strategy, can we characterize the results of following it through time? And they provide necessary and sufficient conditions for a dynamic strategy to satisfy each of these properties.
94 citations
TL;DR: In this paper, the effect of uncertainty on the marginal propensity to consume within the context of the Permanent Income Hypothesis is analyzed. And the marginal investment portfolio for additions to wealth is also characterized.
Abstract: The marginal propensity to consume out of wealth is important for evaluating the effects of taxation on consumption, assessing the possibility of multiple equilibria due to aggregate demand spillovers, and explaining observed variations in consumption. It is also a component of the interest elasticity of consumption and the risk aversion of the value function which gives the expected present value of utility as a function of wealth. This paper analyzes the effect of uncertainty on the marginal propensity to consume within the context of the Permanent Income Hypothesis. Given plausible conditions on the utility function, income risk is found to raise the marginal propensity to consume out of wealth in a multiperiod model with many risky securities. The marginal investment portfolio for additions to wealth is also characterized.
93 citations
01 Jan 2004
TL;DR: In this article, the authors studied the maximization problem of utility from terminal wealth in a multiple-priors model, where asset prices are semimartingales, and proved the existence of a saddle-point for the problem under some suitable conditions on the utility function and the set of priors.
Abstract: This paper studies the maximization problem of utility from terminal wealth in a multiple-priors model, where asset prices are semimartingales. We first state the existence of a saddle-point for our problem, under some suitable conditions on the utility function and the set of priors, which gives the existence of a solution for the maximization problem. A second approach consists in solving a dual minimization problem over the supermartingale measures and different priors. We then consider the case of a Brownian filtration and study in detail the case of a Logarithmic utility function and the case of a Power utility function.
93 citations
Cites background from "Optimum consumption and portfolio r..."
...The problem was studied for the first time by Merton [25] in the case of constant coefficients and treated by markovian methods....
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References
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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