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 set of tools that can be used to manage volatility in revenue growth are presented, and the analysis applies to all jurisdictions that face hard budget constraints and therefore must balance spending increases against revenue growth.
Abstract: Accurately predicting revenue growth is nearly impossible. Predicting the peaks and valleys of the business cycle is even more hopeless. This matters because tax revenues are largely driven by economic growth. Volatile, unpredictable revenue growth causes all sorts of unpleasant responses on the part of governments, most commonly manic-depressive patterns of spending and taxing. Fortunately, modern financial economics gives us a set of tools that can be used to manage volatility. This article shows how such tools can be used to inform fiscal decision making. The focus here is state governments, but the analysis applies to all jurisdictions that face hard budget constraints and therefore must balance spending increases against revenue growth.
41 citations
TL;DR: An analytic model of coral-algal interactions and explicitly considers grazing by herbivorous reef fish is developed and it is determined that the appropriate management policy greatly depends on hurricane frequency and impact level.
Abstract: The interaction between multiple stressors on Caribbean coral reefs, namely, fishing effort and hurricane impacts, is a key element in the future sustainability of reefs. We develop an analytic model of coral–algal interactions and explicitly consider grazing by herbivorous reef fish. Further, we consider changes in structural complexity, or rugosity, in addition to the direct impacts of hurricanes, which are implemented as stochastic jump processes. The model simulations consider various levels of fishing effort corresponding to several hurricane frequencies and impact levels dependent on geographic location. We focus on relatively short time scales so we do not explicitly include changes in ocean temperature, chemistry, or sea level rise. The general features of our approach would, however, apply to these other stressors and to the management of other systems in the face of multiple stressors. It is determined that the appropriate management policy, either local reef restoration or fisheries management, greatly depends on hurricane frequency and impact level. For sufficiently low hurricane impact and macroalgal growth rate, our results indicate that regions with lower-frequency hurricanes require stricter fishing regulations, whereas management in regions with higher-frequency hurricanes might be less concerned with enhancing grazing and instead consider whether local-scale restorative activities to increase vertical structure are cost-effective.
41 citations
Cites background from "Optimum consumption and portfolio r..."
...Jump processes were perhaps first implemented in financial models, in particular by Merton (1971), and are also used in population genetics to describe rare mutations (e.g., Champagnat and Lambert 2007)....
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TL;DR: In this article, the authors consider two hypotheses for the recent performance of real estate returns: the random event argument that real estate is positively correlated with unanticipated inflation and the hedge demand argument that formulates the structural shift hypothesis.
Abstract: In this paper, we consider two hypotheses for the recent performance of real estate returns. The first is the random event argument that real estate is positively correlated with unanticipated inflation but that structural change in expected returns due to a change in the perceived sensitivity of returns to unanticipated inflation has not taken place. The second is the hedge demand argument that formulates the structural shift hypothesis. The paucity of real estate and other expectations data as well as the general identification problem make it extremely difficult to distinguish between these hypothesis. Our tests consist of estimates of inflation betas for various asset categories overtime as well as estimates of the hedge vector, S−1C. Although some support for the hedge argument is found, the results are not strong enough to reject the random event argument and conclude that a decline in the required return on real estate due to a relative increase in inflation beta drove returns during the 1970's.
40 citations
TL;DR: In this paper, the authors study market efficiency in an infinite-horizon model with a monopolistic insider, where the insider can trade with competitive market makers and noise traders, and observes privately the expected growth rate of asset dividends.
Abstract: We study market efficiency in an infinite-horizon model with a monopolistic insider. The insider can trade with competitive market makers and noise traders, and observes privately the expected growth rate of asset dividends. In the absence of the insider, this information would be reflected in prices only after a long series of dividend observations. Thus, the insider’s information is “long-lived.” Surprisingly, however, the monopolistic insider chooses to reveal her information very quickly, within a time converging to zero as the market approaches continuous trading. Although the market converges to strong-form efficiency, the insider’s profits do not converge to zero.
40 citations
TL;DR: In this article, the authors study Merton's portfolio optimization problem in a limit order market and show that the optimal strategy consists of using market orders to keep the proportion of wealth invested in the risky asset within certain boundaries, while within these boundaries limit orders are used to profit from the bid-ask spread.
Abstract: We study Merton’s portfolio optimization problem in a limit order market. An investor trading in a limit order market has the choice between market orders that allow immediate transactions and limit orders that trade at more favorable prices but are executed only when another market participant places a corresponding market order. Assuming Poisson arrivals of market orders from other traders we use a shadow price approach, similar to Kallsen and Muhle-Karbe (Ann Appl Probab, forthcoming) for models with proportional transaction costs, to show that the optimal strategy consists of using market orders to keep the proportion of wealth invested in the risky asset within certain boundaries, similar to the result for proportional transaction costs, while within these boundaries limit orders are used to profit from the bid–ask spread. Although the given best-bid and best-ask price processes are geometric Brownian motions the resulting shadow price process possesses jumps.
40 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