scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Optimum consumption and portfolio rules in a continuous-time model☆

01 Dec 1971-Journal of Economic Theory (Academic Press)-Vol. 3, Iss: 4, pp 373-413
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
Journal ArticleDOI
TL;DR: In this paper, a tractable monetary asset pricing model is proposed, where the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other.
Abstract: This article offers a tractable monetary asset pricing model. In monetary economies, the price level, inflation, asset prices, and the real and nominal interest rates have to be determined simultaneously and in relation to each other. This link allows us to relate in closed form each of the dependent entities to the underlying real and monetary variables. Among other features of such economies, inflation can be partially nonmonetary and the real and nominal term structures can depend on fundamentally different risk factors. In one extreme, the process followed by the real term structure is independent of that followed by its nominal counterpart. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

178 citations


Cites background from "Optimum consumption and portfolio r..."

  • ...To characterize equilibrium relations, further assume, as is standard in the literature [e.g., Grossman and Shiller (1982), Merton (1971) ], that the real asset prices follow a vector diffusion process:...

    [...]

  • ...To characterize equilibrium relations, further assume, as is standard in the literature [e.g., Grossman and Shiller (1982), Merton (1971)], that the real asset prices follow a vector diffusion process: 1pi,t pi,t = µi,t 1t + σi,t Bi,t √ 1t, (11) where µi,t and σi,t are, respectively, the…...

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors study the comovement among stock prices and among exchange rates in a three-good three-country Center-Periphery dynamic equilibrium model in which the Center's agents face portfolio constraints.
Abstract: We study the comovement among stock prices and among exchange rates in a three-good three-country Center-Periphery dynamic equilibrium model in which the Center's agents face portfolio constraints. We characterize equilibrium in closed form for a broad class of portfolio constraints, solving for stock prices, terms of trade, and portfolio holdings. We show that portfolio constraints generate wealth transfers between the Periphery countries and the Center, which increase the comovement of the stock prices across the Periphery. We associate this excess comovement caused by portfolio constraints with the phenomenon known as contagion. The model generates predictions consistent with other important empirical results such as amplification and flight-to-quality effects.

178 citations

Journal ArticleDOI
TL;DR: In this paper, the authors explore the risk-pooling and risk-sharing roles of financial intermediaries and derive some of the operating technologies that can be used to fulfill those roles.
Abstract: The core of financial economic theory is the study of the micro behavior of agents in the intertemporal deployment of their resources in an environment of uncertainty. Economic organizations are regarded as existing primarily to facilitate these allocations and are, therefore, endogenous to the theory. From within the permeable and flexible boundaries of this core, I choose on this occasion to explore the risk-pooling and risk-sharing roles of financial intermediaries and to derive some of the operating technologies that can be used to fulfill those roles. The tool of analysis is the continuous-time model of finance. The focus is on the economic function of financial intermediaries, rather than on their specific institutional structure. Nevertheless, the institutional homes of the financial products and management techniques studied can be readily associated with current structures of banks, investment-management firms, and insurance companies.

178 citations

Journal ArticleDOI
TL;DR: In this article, the authors show that transaction costs can have a first-order effect on liquidity premia and that the presence of transaction costs still cannot fully explain the equity premium puzzle.
Abstract: Standard literature concludes that transaction costs only have a second-order effect on liquidity premia. We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime-switching model in which the investment opportunity set varies over time, we explicitly characterize the optimal consumption and investment strategy. In contrast to the standard literature, we find that transaction costs can have a first-order effect on liquidity premia. However, with reasonably calibrated parameters, the presence of transaction costs still cannot fully explain the equity premium puzzle. TRANSACTION COSTS ARE PREVALENT in almost all financial markets. Extensive research has been conducted on the optimal consumption and investment policy in the presence of transaction costs since the seminal work of Constantinides (1979, 1986). The presence of transaction costs significantly changes optimal consumption and investment strategies. For example, in the presence of transaction costs, continuous trade incurs infinite transaction costs, and thus even a small transaction cost can dramatically decrease the frequency of trade. However, most studies find that the utility loss due to the presence of transaction costs is small. In particular, Constantinides (1986) finds that the liquidity premium (i.e., the maximum expected return an investor is willing to exchange for zero transaction cost) is small relative to the transaction cost, even for a suboptimal trading strategy, and hence concludes that transaction costs only have a second-order effect for asset pricing. Indeed, in this framework it seems unlikely that transaction costs can have an important role in explaining the cross-sectional patterns of expected returns, the equity premium puzzle, or the small stock risk premia. This finding contrasts with many empirical studies that highlight the importance of transaction costs or related measures such as turnover in influencing the cross-sectional patterns of expected returns. 1

177 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of convex transaction costs on consumers' derived utility functions and on optimal consumption and investment decisions is examined in a general multi-period framework and the extent to which multiperiod consumption-investment behavior and capital market equilibrium may be studied in a single period framework is discussed.
Abstract: The effect of convex transactions costs on consumers' derived utility functions and on optimal consumption and investment decisions is examined in a general multiperiod framework. The extent to which multiperiod consumption-investment behavior and capital market equilibrium may be studied in a single period framework is discussed. Optimal investment policy, in terms of a region of no transactions, is shown to be of a particularly simple form.

177 citations

References
More filters
Journal ArticleDOI
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

Book ChapterDOI
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