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 simple model of an exhaustible resource market by allowing the demand function and the reserve level to fluctuate via continuous-time stochastic processes is presented, where producers always know current demand and reserve but do not know what demand and reserves will be in the future.
Abstract: Demand and reserve uncertainty are included in a simple model of an exhaustible resource market by allowing the demand function and the reserve level to fluctuate via continuous-time stochastic processes. Thus, producers always know current demand and reserves but do not know what demand and reserves will be in the future. I show that demand uncertainty has no effect on the expected dynamics of market price, while reserve uncertainty shifts the expected rate of change of price only if extraction costs are nonlinear in reserves. However, if the demand function is nonlinear, both demand, and reserve uncertainty affect the dynamics of production, whatever the character of extraction costs. The model is also extended to include exploration, first as a means of reducing uncertainty and second as a means of accumulating reserves, with uncertainty over the future response of discoveries to exploratory effort.
377 citations
Cites background from "Optimum consumption and portfolio r..."
...Applications to problems in economics can be found in Merton (1969, 1971, 1975) and Fischer (1975)....
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...For a discussion, see Dreyfus (1965), Kushner (1967), Merton (1971), or Chow (1979)....
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TL;DR: This article developed a multi-period rational expectations model of stock trading in which investors have differential information concerning the underlying value of the stock, and examined how trading volume is related to the information flow in the market and how investors' trading reveals their private information.
Abstract: This article develops a multiperiod rational expectations model of stock trading in which investors have differential information concerning the underlying value of the stock. Investors trade competitively in the stock market based on their private information and the information revealed by the market-clearing prices, as well as other public news. We examine how trading volume is related to the information flow in the market and how investors' trading reveals their private information. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
374 citations
TL;DR: A critical review of the literature on the "equity premium puzzle" can be found in this paper, where the authors summarize the historical experience for the USA and other industrialized countries and details the intuition behind the discrepancy between model prediction and empirical data.
Abstract: This paper is a critical review of the literature on the "equity premium puzzle[equal, rising dots]. The puzzle, as originally articulated more than fifteen years ago, underscored the inability of the standard paradigm of Economics and Finance to explain the magnitude of the risk premium, that is, the return earned by a risky asset in excess of the return to a relatively riskless asset such as a U.S. government bond. The paper summarizes the historical experience for the USA and other industrialized countries and details the intuition behind the discrepancy between model prediction and empirical data. Various research approaches that have been proposed to enhance the model's realism are detailed and, as such, the paper reviews the major directions of theoretical financial research over the past ten years. The author argues that the majority of the proposed resolutions fail along crucial dimensions and proposes a promising direction for future research.
373 citations
Posted Content•
TL;DR: In this article, a simple extension of the ordinary American option model which introduces random, exogenous exercise and forfeiture predicts actual exercise times and payoffs just as well as an elaborate utility-maximizing model that explicitly accounts for the nontransferability of options.
Abstract: In theory, hedging restrictions faced by managers make executive stock options more difficult to value than ordinary options, because they imply that exercise policies of managers depend on their preferences and endowments. Using data on option exercises from 40 firms, this paper shows that a simple extension of the ordinary American option model which introduces random, exogenous exercise and forfeiture predicts actual exercise times and payoffs just as well as an elaborate utility-maximizing model that explicitly accounts for the nontransferability of options. The simpler model could therefore be more useful than the preference-based model for valuing executive options in practice.
369 citations
TL;DR: In this paper, a constant proportion portfolio insurance (CPPI) strategy is proposed, which maintains the portfolio's risk exposure a constant multiple of the excess of wealth over a floor, up to a borrowing limit.
368 citations
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