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 article, the authors investigate the intertemporal hedging demands for stocks and bonds for investors in the U.S., Australia, Canada, France, Germany, Italy, and U.K.
45 citations
TL;DR: A survey of problems and methods contained in various works on consumption-investment problems with transaction costs in continuous time, including those of optimal stopping, stochastic singular control, and stochastically impulse control is presented.
Abstract: We present a survey of problems and methods contained in various works on consumption-investment problems with transaction costs in continuous time. The methods are those of optimal stopping, stochastic singular control, and stochastic impulse control. We also describe some open problems in this active area of research.
45 citations
TL;DR: In this paper, the authors consider a portfolio/consumption choice problem in a market model with liquidity risk, where the investor can trade and observe stock prices only at exogenous Poisson arrival times.
Abstract: We consider a portfolio/consumption choice problem in a market model with liquidity risk. The main feature is that the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous stochastic control problem, non-standard in the literature. The dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we provide a convergent numerical algorithm for the resolution to this coupled system of IDE. Several numerical experiments illustrate the impact of the restricted liquidity trading opportunities, and we measure in particular the utility loss with respect to the classical Merton consumption problem.
45 citations
TL;DR: In this article, the impact of drift parameter uncertainty in a basis risk model is explored, where a claim on a non-traded asset is optimally hedged using a correlated traded stock using analytic expansions for indifference prices and hedging strategies.
Abstract: We explore the impact of drift parameter uncertainty in a basis risk model, an incomplete market in which a claim on a non-traded asset is optimally hedged using a correlated traded stock. Using analytic expansions for indifference prices and hedging strategies, we develop an efficient procedure to generate terminal hedging error distributions when the hedger has erroneous estimates of the drift parameters. These show that the effect of parameter uncertainty is occasionally benign, but often very destructive. In light of this, we develop a filtering approach in which the hedger updates her parameter estimates from observations of the asset prices, and we find an analytic soultion to the hedger's combined filtering and control problem in the case that the drift of the traded asset is known with certainty.
45 citations
TL;DR: In this paper, the authors studied optimal household behavior in a model of creative destruction, where the saving technology is characterized by stochastic returns that follow a Poisson process and the equilibrium conditions with optimising households differ substantially from equilibrium conditions where investment in R&D is determined by firms.
Abstract: This paper studies optimal household behaviour in a model of creative destruction. The saving technology is characterised by stochastic returns that follow a Poisson process. It is shown that equilibrium conditions with optimising households differ substantially from equilibrium conditions where investment in R&D is determined by firms. Three out of four market failures disappear and a new market failure resulting from a complementarity in financing R&D is identified. Studying the social optimum shows that it contains as the special case of risk neutrality the social optimum derived in the literature.
45 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