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 developed a model for an investor with multiple priors and aversion to ambiguity, and they characterized the multiple prior by a "confidence interval" around the estimated expected returns.
Abstract: We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive features: (1) it has a solid axiomatic foundation; (2) it is flexible enough to allow for different degrees of uncertainty about expected returns for various subsets of assets and also about the return-generating model; and (3) it delivers closed-form expressions for the optimal portfolio. Our empirical analysis suggests that, compared with portfolios from classical and Bayesian models, ambiguity-averse portfolios are more stable over time and deliver a higher out-of sample Sharpe ratio. (JEL G11) Copyright 2007, Oxford University Press.
505 citations
TL;DR: In this paper, the authors review the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty, and incorporate risk aversion in capacity investment and contrast hedging strategies involving financial versus operational means.
Abstract: This paper reviews the literature on strategic capacity management concerned with determining the sizes, types, and timing of capacity investments and adjustments under uncertainty. Specific attention is given to recent developments to incorporate multiple decision makers, multiple capacity types, hedging, and risk aversion. Capacity is a measure of processing abilities and limitations and is represented as a vector of stocks of various processing resources, while investment is the change of capacity and includes expansion and contraction. After discussing general issues in capacity investment problems, the paper reviews models of capacity investment under uncertainty in three settings:The first reviews optimal capacity investment by single and multiple risk-neutral decision makers in a stationary environment where capacity remains constant. Allowing for multiple capacity types, the associated optimal capacity portfolio specifies the amounts and locations of safety capacity in a processing network. Its key feature is that it is unbalanced; i.e., regardless of how uncertainties are realized, one typically will never fully utilize all capacities. The second setting reviews the adjustment of capacity over time and the structure of optimal investment dynamics. The paper ends by reviewing how to incorporate risk aversion in capacity investment and contrasts hedging strategies involving financial versus operational means.
498 citations
TL;DR: In this paper, the authors employ a martingale approach to study a dynamic consumption-portfolio problem in continuous time with incomplete markets and short-sale constraints, and transform the dynamic problem into a static problem of maximizing expected utility over the consumption bundles.
495 citations
TL;DR: The authors showed that the variance of firms' real gross marginal return on capital has increased significantly, increasing the relative riskiness of investors' returns on equity, and that this can explain a large part of the market decline.
Abstract: Most explanations for the decline in share values over the past two decades have focused on the concurrent increase in inflation.This paper considers an alternative explanation: a substantial increase in the riskiness of capital investments. We show that the variance of firms' real gross marginal return on capital has increased significantly, increasing the relative riskiness of investors' returns on equity, and that this can explain a large part of the market decline. We also assess the effects of increase in the mean and variance of the inflation rate, and a decline in firms' expected return on capital.
495 citations
TL;DR: In this article, it is shown that the results of the domestic capital asset pricing model for each country can be consistent with a single and perfect international market, and that the most realistic description of the international relations of stock prices seems to be a multi-index specification taking into account both national and international factors.
Abstract: THE MARKET STRUCTURE of American stock prices is generally believed to be closely approximated by a single index market model. The MarkowitzSharpe market model assumes that the return on any security is a linear function of the return on the domestic market index. This paper will attempt to determine the International market structure of asset prices. It is doubtful that a single world index model would give a realistic description of the international structure because of the importance of national factors. Therefore several stochastic price processes will be investigated and tested. The most realistic description of the international relations of stock prices seems to be a multi-index specification taking into account both national and international factors. It will also be shown that the results of the domestic capital asset pricing model for each country can be consistent with a single and perfect international market. This study makes use of theoretical framework developed earlier (see Solnik [20]).
492 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