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: It is shown that the optimal policy provides linear frontiers in continuous-time settings where the investor maximizes the expected utility of the terminal wealth in a stochastic market.
36 citations
TL;DR: A simple stochastic control problem whose solution represents the optimal harvest function for managing a renewable resource is investigated and its solution is found to be correct.
Abstract: We investigate a simple stochastic control problem whose solution represents the optimal harvest function for managing a renewable resource.
36 citations
TL;DR: In this paper, the authors used the Capital Asset Pricing Model (CAPM) in several public utility rate cases to measure the cost of equity capital, where the risk premium is obtained as the product of the average annual excess rate of return on a value weighted index of NYSE stocks and an estimate of the utility's NYSE beta.
Abstract: IN RECENT YEARS the Capital Asset Pricing Model (CAPM) has been used in several public utility rate cases to measure the cost of equity capital. In actual application, the cost of equity capital is frequently estimated as the annualized 90 day Treasury Bill rate plus a risk premium. The risk premium is obtained as the product of the average annual excess rate of return on a value weighted index of NYSE stocks (where the average is taken over a long period of time) and an estimate of the utility's NYSE beta. Underlying this procedure is the assumption that risk premiums are strictly proportional to NYSE betas. However, this assumption is inconsistent with the academic empirical literature on CAPM. This literature supports a (non-proportional) linear relationship between risk premiums and NYSE betas with a positive intercept. Other empirical studies suggest that, in addition to betas, risk premiums are influenced by dividend yields and systematic skewness. Evidence presented in this literature is consistent with the predictions of CAPM models that account for margin restrictions on the borrowing of investors, divergent borrowing and lending rates, the existence of risky assets (such as bonds, residential real estate, unincorporated businesses, and human capital) that are not included in the value weighted NYSE stock index, taxes and skewness preference. The version of the CAPM that should be employed in estimating a public utility's cost of equity capital cannot be conclusively demonstrated by theoretical arguments. A positive theory of the valuation of risking assets should not be judged upon the realism of its assumptions but rather on the accuracy of its predictions. The relationship between risk premiums and betas that is used to estimate the cost of equity capital should therefore be estimated econometrically rather than specified a priori. Section 2 compares the predictions of alternative versions of the CAPM. The assertion that risk premiums are proportional to NYSE betas is shown to result in a downward (upward) biased prediction of the cost of equity capital for a public utility having a NYSE beta that is less (greater) than unity, a dividend yield higher (lower) than the yield on the value weighted NYSE stock index, and/or a systematic skewness that exceeds (is less than) its beta. Section 3 discusses problems that arise in implementing CAPM approaches and presents possible solutions. Section 4 describes econometric procedures for
36 citations
TL;DR: In this article, the authors show that such violations can be optimal for risk-averse investors who face portfolio constraints, while the strategy of placing bonds in the tax-deferred account may lead to volatile benefits under different realizations of stock returns.
36 citations
TL;DR: This article found that families with a financially sophisticated husband are more likely to participate in the stock market than those with a wife of equal financial sophistication, best explained by gender norms, which constrain women's influence over intra-household financial decision making.
Abstract: Analyzing microdata covering more than 30 million U.S. households, I document that families with a financially sophisticated husband are more likely to participate in the stock market than those with a wife of equal financial sophistication. This pattern is best explained by gender norms, which constrain women's influence over intra-household financial decision making. Consistent with this interpretation, the baseline effect is attenuated among individuals brought up by working mothers, but becomes stronger among descendants of pre-industrial societies in which women specialized in activities within the home and households with a husband born and raised in a southern state. A randomized controlled experiment further reveals that female identity hinders idea contribution by the wife. In contrast, male identity causes men to be less open to an opposing viewpoint of their wife, even if her proposition is optimal. These findings suggest that gender identity norms can have real consequences for household financial well-being.
35 citations
Cites background from "Optimum consumption and portfolio r..."
...(3)The stylized fact in the literature is that stock market participation is far from universal as prescribed by canonical models of lifetime consumption and portfolio choice (Merton, 1971; Haliassos and Bertaut, 1995)....
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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