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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
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Journal ArticleDOI
TL;DR: In this article, the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes is considered.
Abstract: We consider the problem of optimal investment and consumption in a class of multidimensional jump-diffusion models in which asset prices are subject to mutually exciting jump processes. This captures a type of contagion where each downward jump in an asset's price results in increased likelihood of further jumps, both in that asset and in the other assets. We solve in closed-form the dynamic consumption-investment problem of a log-utility investor in such a contagion model, prove its optimality and discuss features of the solution, including flight-to-quality. The clustering of jumps gives rise to a time-varying optimal asset allocation: as jumps predict more jumps, the portfolio should be optimally rebalanced to hedge the risk of future jumps. The exponential and power utility investors are also considered: in these cases, the optimal strategy can be characterized as a distortion of the strategy of a corresponding non-contagion investor.

63 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduce a new estimation for the dynamics of betas, which combines two previously separate approaches in the literature, data-driven filters and parametric methods.
Abstract: This paper introduces a new estimation for the dynamics of betas. It combines two previously separate approaches in the literature, data-driven filters and parametric methods. Namely, we show how to estimate the parametric beta dynamics by instrumental variables combined with block-sampling - but not overlapping window filters - of data-driven betas. Instrumental variables are needed because of the measurement errorsin empirical betas. We find that, while betas are very strongly autocorrelated, neither aggregate nor firm-specific variables explain much of their quarterly variation. We then compare block-samplers and overlapping window filters using a criterion of economic significance. Namely, we track the out-of-sample performance of portfolios optimized subject to target beta constraints. For target betas of zero, the case of many hedge funds, we show that estimation error results in systematic overshooting of the target beta. These portfolios benefit from the use of medium to long term estimation windows of daily returns.

62 citations


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

  • ...There are several variations on the Fama and MacBeth procedure, and Foster and Nelson (1996) provide a unified approach that describes the various rolling and blocksampling schemes that have been considered....

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  • ...First, we start with the approach in Foster and Nelson (1996), centered on rolling sample estimators....

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Journal ArticleDOI
TL;DR: In this paper, the authors systematically analyze the review and critique of this important area and broadly to discuss the customer portfolio theories and their implications in reference to marketing and purchasing perspectives, and provide an insight of how marketers interpret and describe companies' actions and the discussion provides a framework for relationship management.
Abstract: Purpose – The customer portfolio and relationship management have been of contemporary interest to the academics and practitioners. This paper aims to systematically analyze the review and critique of this important area and broadly to discuss the customer portfolio theories and their implications in reference to marketing and purchasing perspectives.Design/methodology/approach – The major conceptual contributions in the area of customer portfolio and relationship management have been categorically analyzed in the paper. The paper provides an insight of how marketers interpret and describe companies' actions and the discussion provides a framework for relationship management, the central tenet of which is to enable managers to invest their resources in the most efficient and effective way.Findings – The review of literature shows that the customer portfolio analysis can provide strategic input to the firm towards developing a successful planning process. The conceptual discussion in the paper on relations...

62 citations

Journal ArticleDOI
TL;DR: This article examined the characteristics of informal investors in Singapore and analyzed the key determinant factors that differentiate individuals who become informal investors from those who do not make informal investments, and investigated the differences between determinants of higher and lower value investment propensities.
Abstract: Since Wetzel (1982, 1983) identified the business angel as a primary source of risk capital, there has been increased interest in the role of informal investors in the formation of new business ventures in the developed OECD countries. However, there remains little known about informal investors in developing or newly industrialized economies such as Singapore. Based on data collected using the Global Entrepreneurship Monitor (GEM) methodology (Reynolds et al., 2002), this paper examines the characteristics of informal investors in Singapore, and analyses the key determinant factors that differentiate individuals who become informal investors from those who do not make informal investments. In particular, we examine if these factors differ depending on the relationship between the investor and entrepreneur. We also investigate the differences between determinants of higher and lower value investment propensities. The findings reveal that knowing entrepreneurs personally was the factor with the st...

62 citations

Journal ArticleDOI
TL;DR: It is demonstrated that, by means of an example, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa and an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions.
Abstract: We generalize Markowitz analysis to the situations involving an uncertain exit time. Our approach preserves the form of the original problem in that an investor minimizes portfolio variance for a given level of the expected return. However, inputs are now given by the generalized expressions for mean and variance-covariance matrix involving moments of the random exit time in addition to the conditional moments of asset returns. Although efficient frontiers in the generalized and the standard Markowitz case may coincide under certain conditions, we demonstrate that, by means of an example, in general that is not true. In particular, portfolios efficient in the standard Markowitz sense can be inefficient in the generalized sense and vice versa. As a result, an investor facing an uncertain time horizon and investing as if her time of exit is certain would in general make suboptimal portfolio allocation decisions. Numerical simulations show that a significant efficiency loss can be induced by an improper use of standard mean-variance analysis when time horizon is uncertain.

62 citations


Cites background or methods or result from "Optimum consumption and portfolio r..."

  • ...…the solution in the standard case (to make the comparison easier, we have used a standard notation adopted, for example, in Huang and Litzenberger 1988).12 This result can be seen as i) a confirmation and ii) an extension of a result derived by Merton (1971) and Richard (1975) in a dynamic setup....

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  • ...Namely, when exit time is independent of the portfolio composition, an investor’s utility function belongs to the class of HARA utilities (quadratic utility is a member of that class), and the risky assets prices follow Geometric Brownian Motion, Merton (1971) demonstrates that the optimal portfolio consumption problem with continuous rebalancing maps into the infinite-horizon problem with a re-normalized subjective discount factor....

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  • ...This result both confirms and extends the result in Merton (1971) (see the discussion in Section 4)....

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  • ...Merton (1971), as a special case, also addresses a dynamic optimal portfolio selection problem for an investor retiring at an uncertain date, defined as the date of the first jump of a Poisson process with constant intensity....

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  • ...13 - Merton (1971) and Richard (1975) assume that asset returns are driven by a geometric Brownian motion, hence ruling out a possible deviation from the random walk....

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References
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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