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, the effects of corruption using an open economy version of the endogenous growth model with international capital mobility is studied. And the authors test empirically the predictions of the theory using a sample of 142 countries for the period 1994-2014 and GMM methods.
130 citations
TL;DR: In this article, the authors discuss portfolio balance models with postulated asset demands, asset demands broadly consistent with but not directly implied by microeconomic theory, and discuss that the consumer arrives at his or her asset demands by maximizing his or their utility given interest rates and the parameters of the distributions of prices and exchange rates.
Abstract: Publisher Summary This chapter discusses portfolio balance models with postulated asset demands, asset demands broadly consistent with but not directly implied by microeconomic theory. The demand for the sum of assets denominated in each currency is homogeneous of degree one in nominal wealth, and the demand for money in each country depends on the return on the security denominated in that country's currency but not on the return on securities denominated in other currencies. However, under these same assumptions the demand for money depends on real wealth. Because the conclusions of macroeconomic analysis often depend crucially on the form of asset demand functions, it is important to continue to explore the implications of the microeconomic theory and other microeconomic approaches. The chapter discusses that the consumer arrives at his or her asset demands by maximizing his or her utility given interest rates and the parameters of the distributions of prices and exchange rates. The distributions of prices and exchange rates are not invariant to changes in the distributions of policy variables and stochastic components of tastes and technology. It has been recognized that a very important item on the research agenda is imbedding consumer's asset demands based on utility maximization in a general equilibrium model in which the distributions of prices and exchange rates are determined endogenously.
129 citations
TL;DR: In this article, a double adjustment as households age is documented: a rebalancing of the portfolio composition away from stocks as they approach retirement and stock market exit after retirement, and a yearly probability of a large stock market loss in line with the frequency of stock market crashes in Norway.
Abstract: Using error-free data on life-cycle portfolio allocations of a large sample of Norwegian households, we document a double adjustment as households age: a rebalancing of the portfolio composition away from stocks as they approach retirement and stock market exit after retirement. When structurally estimating an extended life-cycle model, the parameter combination that best fits the data is one with a relatively large risk aversion, a small per-period participation cost, and a yearly probability of a large stock market loss in line with the frequency of stock market crashes in Norway.
128 citations
TL;DR: In this article, the authors define the spanning number of the economy as the fewest number of security markets required to sustain a complete markets equilibrium (in a dynamic sense made precise in the paper).
Abstract: Stochastic equilibria under uncertainty with continuous-time security trading and consumption are demonstrated in a general setting. A common question is whether the current price of a security is an unbiased predictor of the future price of the security plus intermediate dividends. This is the hypothesis of "no expected financial gains from trade." The relevance of this hypothesis in multi-good economies is called into question by the following demonstrated fact. For each set of probability assessments there exists a corresponding equilibrium, one with the original agents, original equilibrium allocations, and no expected financial gains from trade under the given probability assessments. The spanning number of the economy is defined as the fewest number of security markets required to sustain a complete markets equilibrium (in a dynamic sense made precise in the paper). The spanning number is linked directly to agent primitives, in particular the manner in which new information resolves uncertainty over time. The spanning number is shown to be invariant under bounded changes in expectations. Several examples are given in which the spanning number is finite even though the number of potential states of the world is infinite.
128 citations
TL;DR: In this article, a general model of optimal choice over risky assets is used to derive an estimable exchange rate equation which is then applied to the German mark-U.S. dollar and Japanese yen U.S dollar exchange rates over the period 1974 to 1988.
127 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