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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Book•
25 Dec 2005
TL;DR: In this paper, the authors look at the distribution of income and wealth and the effects that this has on the macroeconomy, and vice versa, taking stock of results and methods developed in the context of the 1990s revival of growth theory, the authors focus on capital accumulation and long-run growth.
Abstract: This book looks at the distribution of income and wealth and the effects that this has on the macroeconomy, and vice versa. Is a more equal distribution of income beneficial or harmful for macroeconomic growth, and how does the distribution of wealth evolve in a market economy? Taking stock of results and methods developed in the context of the 1990s revival of growth theory, the authors focus on capital accumulation and long-run growth. They show how rigorous, optimization-based technical tools can be applied, beyond the representative-agent framework of analysis, to account for realistic market imperfections and for political-economic interactions. The treatment is thorough, yet accessible to students and nonspecialist economists, and it offers specialist readers a wide-ranging and innovative treatment of an increasingly important research field. The book follows a single analytical thread through a series of different growth models, allowing readers to appreciate their structure and crucial assumptions. This is particularly useful at a time when the literature on income distribution and growth has developed quickly and in several different directions, becoming difficult to overview.
206 citations
Posted Content•
TL;DR: In this paper, the authors focus on tests of whether measures of illiquidity, which are likely to be correlated with the noise, are priced in the cross-section of stock returns.
Abstract: Microstructure noise in security prices biases the results of empirical asset pricing specifications, particularly when security-level explanatory variables are cross-sectionally correlated with the amount of noise. We focus on tests of whether measures of illiquidity, which are likely to be correlated with the noise, are priced in the cross-section of stock returns, and document a significant upward bias in estimated return premia for an array of illiquidity measures in CRSP monthly return data. The upward bias is larger when illiquid securities are included in the sample, but persists even for NYSE/AMEX stocks after decimalization. We introduce a methodological correction to eliminate the biases that simply involves WLS rather than OLS estimation, and find evidence of smaller, but still significant, return premia for illiquidity after implementing the correction.
204 citations
TL;DR: It is proved the existence and uniqueness of an "equilibrium" commodity spot price process and productive asset prices and when the agents solve their individual optimization problems using the equilibrium prices, all of the commodity is exactly consumed as it is received and the financial markets are in zero net supply.
Abstract: We consider an economy in which a set of agents own productive assets which provide commodity dividend streams, and the agents also receive individual commodity income streams, over a finite time horizon. The agents can buy and sell the commodity at a certain spot price and buy and sell their shares of the productive assets. The proceeds can be invested in financial assets whose prices are modelled as semimartingales. Each agent's objective is to choose a commodity consumption process and to manage his portfolio so as to maximize the expected utility of his consumption, subject to having nonnegative wealth at the terminal time. We derive the optimal agent consumption and investment decision processes when the prices of the productive assets and commodity spot prices are specified. We prove the existence and uniqueness of an "equilibrium" commodity spot price process and productive asset prices. When the agents solve their individual optimization problems using the equilibrium prices, all of the commodity is exactly consumed as it is received, all of the productive assets are exactly owned and the financial markets are in zero net supply.
203 citations
TL;DR: In this paper, the authors examine government debt and tax-transfer policies that can be improved the allocation of risk between generations, and they provide a non-Keynesian justification for the debt-finance of wars and recessions, as well as an added rationale for Social Security type tax transfer schemes which aid unlucky generations, e.g. the Depression generation, at the expense of luckier generations.
203 citations
Posted Content•
TL;DR: This paper presented a dynamic equilibrium model of bond markets in which two groups of agents hold heterogeneous expectations about future economic conditions, which cause agents to take speculative positions against each other and therefore generate endogenous relative wealth fluctuation.
Abstract: This paper presents a dynamic equilibrium model of bond markets in which two groups of agents hold heterogeneous expectations about future economic conditions. The heterogeneous expectations cause agents to take speculative positions against each other and therefore generate endogenous relative wealth fluctuation. The relative wealth fluctuation amplifies asset price volatility and contributes to the time variation in bond premia. Our model shows that a modest amount of heterogeneous expectation can help explain several puzzling phenomena, including the "excessive volatility" of bond yields, the failure of the expectations hypothesis, and the ability of a tent-shaped linear combination of forward rates to predict bond returns.
203 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