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.
Citations
More filters
TL;DR: In the context of an economy with rational expectations, Mehra and Prescott as discussed by the authors showed that the problem of the equity premium puzzle can be solved by relaxing the time separability of von Neumann-Morgenstern preferences to allow for adjacent complementarity in consumption.
Abstract: The equity premium puzzle, identified by Mehra and Prescott, states that, for plausible values of the risk aversion coefficient, the difference of the expected rate of return on the stock market and the riskless rate of interest is too large, given the observed small variance of the growth rate in per capita consumption. The puzzle is resolved in the context of an economy with rational expectations once the time separability of von Neumann-Morgenstern preferences is relaxed to allow for adjacent complementarity in consumption, a property known as habit persistence. Essentially habit persistence drives a wedge between the relative risk aversion of the representative agent and the intertemporal elasticity of substitution in consumption.
1,895 citations
TL;DR: In this article, the authors review some basic models of irreversible investment to illustrate the option-like characteristics of investment opportunities, and show how optimal investment rules can be obtained from methods of option pricing, or alternatively from dynamic programming.
Abstract: Despite its importance to economic growth and the evolution of market structure, the investment behavior of firms, industries, and countries remains poorly understood. This paper has several objectives. First, it reviews some basic models of irreversible investment to illustrate the option-like characteristics of investment opportunities, and to show how optimal investment rules can be obtained from methods of option pricing, or alternatively from dynamic programming. Second, it discusses the implication of irreversibility for the empirical analysis of investment behavior. Finally, it discusses briefly some of the implications that the irreversibility of investment may have for policy. For example, policies that stabilize prices or exchange rates may be effective ways of stimulating investment.
1,797 citations
TL;DR: In this paper, the authors test the pecking order theory of corporate leverage on a broad cross-section of publicly traded American firms for 1971 to 1998 and find that net equity issues track the financing deficit more closely than do net debt issues.
1,783 citations
TL;DR: Discount-rate variation is the central organizing question of current asset-pricing research as discussed by the authors, and a survey of discount-rate theories and applications can be found in the survey.
Abstract: Discount-rate variation is the central organizing question of current asset-pricing research. I survey facts, theories, and applications. Previously, we thought returns were unpredictable, with variation in price-dividend ratios due to variation in expected cashflows. Now it seems all price-dividend variation corresponds to discount-rate variation. We also thought that the cross-section of expected returns came from the CAPM. Now we have a zoo of new factors. I categorize discount-rate theories based on central ingredients and data sources. Incorporating discount-rate variation affects finance applications, including portfolio theory, accounting, cost of capital, capital structure, compensation, and macroeconomics.
1,624 citations
TL;DR: In this article, a martingale technique is employed to characterize optimal consumption-portfolio policies when there exist nonnegativity constraints on consumption and on final wealth, and a way to compute and verify optimal policies is provided.
1,606 citations
Cites background or methods from "Optimum consumption and portfolio r..."
...Merton (1971) is the pioneering paper in this regard....
[...]
...This procedure will l)e demonstrated in the next section in the context of the model of Merton (1971)....
[...]
...In Section 3, we specialize the general model of Section 2 to a model considered originally by Merton (1971)....
[...]
...We now specialize our general model of uncertainty developed i Section 2 to the model considered by Merton (1971) and revisited recently )y Karatzas, Lehoczky, Sethi, and Shreve (1986)....
[...]
...In the unconstrained case given in Merton (1971), the optimal policies for HARA utility functions are linear in wealth; when nonnegativity constraints are included, this is no longer true....
[...]
References
More filters
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