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 the context of managing downside correlations, this paper examined the use of multi-dimensional elliptical and asymmetric copula models to forecast returns for portfolios with 3-12 constituents.
Abstract: In the context of managing downside correlations, we examine the use of multi-dimensional elliptical and asymmetric copula models to forecast returns for portfolios with 3–12 constituents. Our analysis assumes that investors have no short-sales constraints and a utility function characterized by the minimization of Conditional Value-at-Risk (CVaR). We examine the efficient frontiers produced by each model and focus on comparing two methods for incorporating scalable asymmetric dependence structures across asset returns using the Archimedean Clayton copula in an out-of-sample, long-run multi-period setting. For portfolios of higher dimensions, we find that modeling asymmetries within the marginals and the dependence structure with the Clayton canonical vine copula (CVC) consistently produces the highest-ranked outcomes across a range of statistical and economic metrics when compared to other models incorporating elliptical or symmetric dependence structures. Accordingly, we conclude that CVC copulas are ‘worth it’ when managing larger portfolios.
115 citations
TL;DR: Methods of risk sensitive impulsive control theory are developed in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter.
Abstract: This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska.
115 citations
TL;DR: The authors analyzes the pricing of stock index options in a simple general equilibrium model, where the volatility of the stock index and the spot rate of interest are functions of a stochastic variable, and investigates the biases that arise when using the Black-Scholes model with the assumed volatility and interest rate dynamics.
Abstract: This paper analyzes the pricing of stock index options in a simple general equilibrium model. In this model, the volatility of the stock index and the spot rate of interest are functions of a stochastic variable. The paper investigates the biases that arise when using the Black-Scholes model with the assumed volatility and interest rate dynamics. It is shown that the model can, in principle, explain the biases observed in empirical work on stock index options.
115 citations
Cites background from "Optimum consumption and portfolio r..."
...4 See, for instance, Merton (1971). 5 See Breeden (1986) for an extensive discussion of the relation between production risks and the rate of interest....
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TL;DR: In this article, contingent claim valuation in a Lucas-type exchange economy is studied and the derived fundamental valuation equation differs from its Cox-Ingersoll-Ross production-economy counterpart in that it is expressed in terms of the direct utility function and an exogenous output process, thus offering superior tractability.
114 citations
TL;DR: In this paper, the authors examine local and global approximation methods that have been used or have potential future value in economic and econometric analysis, and demonstrate their application to dynamic economic analysis, dynamic games, and asset market equilibrium with asymmetric information.
Abstract: Publisher Summary This chapter examines local and global approximation methods that have been used or have potential future value in economic and econometric analysis. The chapter presents the related projection method for solving operator equations and illustrates its application to dynamic economic analysis, dynamic games, and asset market equilibrium with asymmetric information. In the chapter, it is shown that a general class of techniques from the numerical partial differential equations literature can be usefully applied and adapted to solve nonlinear economic problems. Despite the specificity of the applications discussed in the chapter the general description makes clear the general usefulness of perturbation and projection methods for economic problems, both theoretical modeling and empirical analysis. The application of perturbation and projection methods and the underlying approximation ideas have substantially improved the efficiency of economic computations. In addition, exploitation of these ideas will surely lead to progress.
114 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