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 model of fundamentalists and chartists is proposed to generate a number of dynamic regimes which are compatible with the empirical evidence of the random walk theory of asset prices.
Abstract: A number of recent empirical studies cast some doubt on the random walk theory of asset prices and suggest these display significant transitory components and complex chaotic motion. This paper analyses a model of fundamentalists and chartists which can generate a number of dynamic regimes which are compatible with the recent empirical evidence.
265 citations
TL;DR: In this paper, a model of the joint investment in financial wealth and human wealth was developed to show that human capital investment is an inverse function of the degree of relative risk aversion.
Abstract: Risk aversion enters many theoretical models of human capital investment, but attitudes toward risk have not been incorporated in empirical models of human capital investment. This article develops a model of the joint investment in financial wealth and human wealth to show that human capital investment is an inverse function of the degree of relative risk aversion. Using data from the Survey of Consumer Finances, I find that wage growth is positively correlated with preferences for risk taking. More-educated individuals are also more likely to be risk takers, thus risk taking explains a portion of the returns to education.
264 citations
TL;DR: In this paper, the authors study convergence traders with logarithmic utility in a continuous-time equilibrium model and show that when an unfavorable shock causes them to suffer capital losses, thus eroding their risk-bearing capacity, they liquidate their positions, thereby amplifying the original shock.
264 citations
Cites background from "Optimum consumption and portfolio r..."
...This trading strategy is also myopic, i.e., there is no hedging demand (against changes in the future investment opportunity set), as discussed in Merton (1971) and Breeden (1979)....
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...This trading strategy is also myopic, i.e., there is no hedging demand (against changes in the future investment opportunity set), as discussed in Merton (1971) and Breeden (1979)....
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TL;DR: In this article, the authors identify the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations, and con-struct a general equilibrium "difference-of-opinion" model of sentiment in which there are two classes of agents, one of which is overconfident about a public signal, while still optimizing intertemporally.
Abstract: Our objective is to identify the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations. We con struct a general equilibrium "difference-of-opinion" model of sentiment in which there are two classes of agents, one of which is overconfident about a public signal, while still optimizing intertemporally. Overconfident investors overreact to the signal and introduce an additional risk factor causing stock prices to be excessively volatile. Con sequently, rational investors choose a conservative portfolio; moreover, this portfolio depends not just on the current price divergence but also on their prediction about
261 citations
TL;DR: In this paper, the Merton portfolio management problem in the context of non-exponential discounting is investigated, where the decision-maker at time t = 0 can choose the policy that is optimal from her point of view, and constrain the others to abide by it, although they do not see it as optimal for them.
Abstract: In this paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting. This gives rise to time-inconsistency of the decision-maker. If the decision-maker at time t = 0 can commit her successors, she can choose the policy that is optimal from her point of view, and constrain the others to abide by it, although they do not see it as optimal for them. If there is no commitment mechanism, one must seek a subgame-perfect equilibrium policy between the successive decision-makers. In the line of the earlier work by Ekeland and Lazrak (Preprint, 2006) we give a precise definition of equilibrium policies in the context of the portfolio management problem, with finite horizon. We characterize them by a system of partial differential equations, and establish their existence in the case of CRRA utility. An explicit solution is provided for the case of logarithmic utility. We also investigate the infinite-horizon case and provide two different equilibrium policies for CRRA utility (in contrast with the case of exponential discounting, where there is only one optimal policy). Some of our results are proved under the assumption that the discount function h(t) is a linear combination of two exponentials, or is the product of an exponential by a linear function.
260 citations
Cites background from "Optimum consumption and portfolio r..."
...The ground-breaking paper in this literature is Merton [11]....
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References
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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