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, a dealer in U.S. Government securities is assessed directly and then estimated statistically from his actual demand for bills in the weekly Treasury auctions, based on the forecasts made by the dealer himself.
Abstract: SINCE ITS INTRODUCTION, the expected utility hypothesis has been widely used in the construction of economic models. More recently, attention has focused on the conditions under which it is possible in principle to recover individual investors' risk preferences from their demand for assets (Dybvig and Polemarchakis [2]). This paper represents a first attempt to recover preferences operationally from data on the actual demand for assets. Numerous difficulties are encountered in attempting to measure preferences toward risk in a real world setting. Preferences are revealed through the choices of an individual. But in an uncertain world, these choices also depend on his expectations of future events. Hence, an immediate problem arises in separating the influences of each on such decisions. Problems can also arise in measuring other variables, such as wealth, which influence choices. Because of these difficulties, efforts to classify and measure an individual's risk preferences have been confined to direct assessments in hypothetical environments (e.g. Kahneman and Tversky [4] and Keeney and Raiffa [5, pp. 203-212]).2 In these studies the authors assumed that stated preferences are accurate indicators of actual behavior. The question remains, however, whether individuals actually behave in the way their assessments predict. The purpose of this note is to make some progress in answering this question. In it an experiment is described which infers an individual's risk preferences from his actual choices in a real world environment. Specifically, the risk aversion of a dealer in U.S. Government securities is assessed directly and then estimated statistically from his actual demand for bills in the weekly Treasury auctions. The distribution of returns used in the analysis are calculated from the forecasts made by the dealer himself. In addition to introducing new procedures for measuring preferences, this study provides insights into the reliability of direct assessments in predicting the actual behavior.
86 citations
TL;DR: In this paper, the optimal portfolio, consumption-leisure and retirement choice of an infinitely-lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure is studied.
Abstract: We study optimal portfolio, consumption-leisure and retirement choice of an infinitely lived economic agent whose instantaneous preference is characterized by a constant elasticity of substitution (CES) function of consumption and leisure. We integrate in one model the optimal consumption-leisure-work choice, the optimal portfolio selection, and the optimal stopping problem in which the agent chooses her retirement time. The economic agent derives utility from both consumption and leisure, and is able to adjust her supply of labor flexibly above a certain minimum work-hour, and also has a retirement option. We solve the problem analytically by considering a variational inequality arising from the dual functions of the optimal stopping problem. The optimal retirement time is characterized as the first time when her wealth exceeds a certain critical level. We provide the critical wealth level for retirement and characterize the optimal consumption-leisure and portfolio policies before and after retirement in closed forms. We also derive properties of the optimal policies. In particular, we show that consumption in general jumps around retirement.
86 citations
TL;DR: In this paper, the authors examined the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value.
Abstract: We examine the Morton and Pliska (1993) model for the optimal management of a portfolio when there are transaction costs proportional to a fixed fraction of the portfolio value. We analyze this model in the realistic case of small transaction costs by conducting a perturbation analysis about the no-transaction-cost solution. Although the full problem is a free-boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility.
86 citations
TL;DR: In this article, the authors consider a dynamic active portfolio management problem where the objective is related to the tradeoff between the achievement of performance goals and the risk of a shortfall, and the resulting optimal policy is a state-dependent policy that provides new insights.
Abstract: Active portfolio management is concerned with objectives related to the outperformance of the return of a target benchmark portfolio. In this paper, we consider a dynamic active portfolio management problem where the objective is related to the tradeoff between the achievement of performance goals and the risk of a shortfall. Specifically, we consider an objective that relates the probability of achieving a given performance objective to the time it takes to achieve the objective. This allows a new direct quantitative analysis of the risk/return tradeoff, with risk defined directly in terms of probability of shortfall relative to the benchmark, and return defined in terms of the expected time to reach investment goals relative to the benchmark. The resulting optimal policy is a state-dependent policy that provides new insights. As a special case, our analysis includes the case where the investor wants to minimize the expected time until a given performance goal is reached subject to a constraint on the shortfall probability.
86 citations
TL;DR: In this article, the authors numerically solve the decision problem of a multi-period constant relative risk aversion individual who faces transaction costs and has access to two risky assets, both with predictable returns.
Abstract: This paper numerically solves the decision problem of a multiperiod constant relative risk aversion individual who faces transaction costs and has access to two risky assets, both with predictable returns. With proportional transaction costs and independent and identically distributed returns, we numerically find the rebalancing rule to be a no-trade region for the portfolio weights with rebalancing to the boundary. The shape of the no-trade region depends on the correlation between the two risky assets. With predictable returns, there is instead a no-trade region for each state. We also examine several important economic questions, including the utility cost of not being able to buy on margin or short stock.
85 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