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Journal ArticleDOI

Optimum consumption and portfolio rules in a continuous-time model☆

01 Dec 1971-Journal of Economic Theory (Academic Press)-Vol. 3, Iss: 4, pp 373-413
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.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors apply the principle of equivalent utility to price and reserve equity-indexed life insurance, as introduced by Gerber (1976) and extended by Moore and Young (2002a, b).
Abstract: The author applies the principle of equivalent utility to price and reserve equity-indexed life insurance. Young and Zariphopoulou (2002a, b) extended this principle to price insurance products in a dynamic framework. However, in those papers, the insurance risks were independent of the risky asset in the financial market. By contrast, the death benefit for equity-indexed life insurance is a function of a risky asset; therefore, this paper further extends the principle of equivalent utility. In a second extension, the author applies the principle of equivalent utility to calculate reserves, as introduced by Gerber (1976). In a related paper, Moore and Young (2002) price equity-indexed pure endowments, the building blocks of equity-indexed life annuities.

46 citations

Journal ArticleDOI
TL;DR: In this paper, a stock-bond-cash portfolio problem of a risk-and ambiguity-averse investor when interest rates and the inflation rate are stochastic is solved.
Abstract: We solve, in closed form, a stock-bond-cash portfolio problem of a risk- and ambiguity-averse investor when interest rates and the inflation rate are stochastic. The expected inflation rate is unobservable, but the investor can learn about it from observing realized inflation and stock and bond prices. The investor is ambiguous about the inflation model and prefers a portfolio strategy which is robust to model misspecification. Ambiguity about the inflation dynamics is shown to affect the optimal portfolio fundamentally different than ambiguity about the price dynamics of traded assets, for example the optimal portfolio weights can be increasing in the degree of ambiguity aversion. In a numerical example, the optimal portfolio is significantly affected by the learning about expected inflation and somewhat affected by ambiguity aversion. The welfare loss from ignoring learning or ambiguity can be considerable.

46 citations

Journal ArticleDOI
TL;DR: In this paper, a decade worth of variance swap rate quotes at five maturities were obtained and the information in both the time series and the term structure of the variance swap rates were exploited to analyze the return variance rate dynamics and market pricing of variance risk.
Abstract: With increasing appreciation of the fact that stock return variance is stochastic and variance risk is heavily priced, the industry has created a series of variance derivative products to span variance risk. The variance swap contract is the most actively traded of these products. It pays at expiry the difference between the realized return variance and a fixed rate, called the variance swap rate, determined at the inception of the contract. We obtain a decade worth of variance swap rate quotes at five maturities. With the data, we first exploit the information in both the time series and the term structure of the variance swap rates to analyze the return variance rate dynamics and market pricing of variance risk. We then study both theoretically and empirically how investors can use variance swap contracts across different maturities to span the variance risk and to revise their dynamic asset allocation decisions. We find that with the swap contract to span the variance risk, an investor increases her investment in the underlying stock. In addition, the investor's indirect utility increases significantly when allowed to span the volatility risk using variance swap contracts. Finally, an out-of-sample study confirms that the gains from including variance swaps into the portfolio mix are large.

46 citations


Cites background from "Optimum consumption and portfolio r..."

  • ...(41) As shown in Merton (1971), the optimal allocation to risky asset includes two components: a myopic component that is proportional to the mean excess return andan intertemporal hedging demand that is proportional to the covariance between the risky asset returnsand the state variables that…...

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  • ...As shown in the seminal paper of Merton (1971), the optimal allocation to risky assets includes two components: a myopic component that is proportional to the mean excess return and an intertemporal hedging demand that is proportional to the covariance between the risky asset returns and the state variables that govern the stochastic investment opportunity, both scaled by the covariance matrix of the asset return....

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Posted Content
TL;DR: In this article, the authors developed a unified framework based on human capital in order to enable individual investors to make both decisions jointly and investigate the impact of the magnitude of human capital, its volatility, and its correlation with other assets as well as bequest preferences and subjective survival probabilities on the optimal portfolio of life insurance and traditional asset classes.
Abstract: Financial planners and advisors have recently started to recognize that human capital must be taken into account when building optimal portfolios for individual investors. But human capital is not just another pre-endowed asset class that must be included as part of the portfolio frontier. An investor's human capital contains a unique mortality risk, which is the loss of all future income and wages in the unfortunate event of premature death. However, life insurance in its various guises and incarnations can hedge against this mortality risk. Thus, human capital affects both the optimal asset allocation and the optimal demand for life insurance. Yet historically, asset allocation and life insurance decisions have consistently been analyzed separately both in theory and practice. In this paper, we develop a unified framework based on human capital in order to enable individual investors to make both decisions jointly. We investigate the impact of the magnitude of human capital, its volatility, and its correlation with other assets as well as bequest preferences and subjective survival probabilities on the optimal portfolio of life insurance and traditional asset classes. We do this through five case studies that implement our model. Indeed, our analysis validates some intuitive rules of thumb but provides additional results that are not immediately obvious.

46 citations


Cites background from "Optimum consumption and portfolio r..."

  • ...In our model, the investor adjusts the financial portfolio to compensate for nontradable risk exposures in human capital (Merton 1971; Bodie, Merton, and Samuelson 1992; Heaton and Lucas 1997; Jagannathan and Kocherlakota 1996; Campbell and Viceira 2002)....

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Journal ArticleDOI
TL;DR: In this paper, a model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is formulated in which the vector process representing returns to investments is a general semimartingale.
Abstract: A model of optimal accumulation of capital and portfolio choice over an infinite horizon in continuous time is formulated in which the vector process representing returns to investments isa general semimartingale. Methods of stochastic calculus and calculus of variations are used to obtain necessary and sufficient conditions for optimality involving martingale properties ofthe shadow price processes associated with alternative portfolio cum saving plans.The relationship between such conditions and portfolio equations is investigated.The results are appliedtospecial cases where the returns process has stationary independent increments and the utility function has the discounted relative risk aversion form

46 citations

References
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Journal ArticleDOI
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

Book ChapterDOI
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