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 optimal asset allocation strategy of a power utility investor who can invest in cash (a bank account), nominal bonds, and stocks (the stock index) in a model that exhibits mean-reverting stock returns and real interest rate uncertainty is provided.
120 citations
TL;DR: In this article, the authors consider an extension of the Merton optimal investment problem, where the conditional distribution function of an agent's time-horizon is stochastic and correlated to returns on risky securities.
120 citations
Cites background or methods or result from "Optimum consumption and portfolio r..."
...Merton (1971), as a special case, also addresses a dynamic optimal portfolio selection problem for an investor retiring at an uncertain date, defined as the date of the first jump of an independent Poisson process with constant intensity....
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...In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton (1971), where we allow the conditional distribution function of an agent’s time horizon to be stochastic and correlated to returns on risky securities....
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...In this framework, we confirm and extend a result obtained by Merton (1971) and Richard (1975), as we show that the optimal portfolio selection is not affected by the presence of an uncertain time horizon, even though the value function is not identical to the one corresponding to the standard…...
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...In order to address this question, we consider a suitable extension of the familiar optimal investment problem of Merton (1971), where we allow the conditional distribution function of an agent’s time horizon to be stochastic and correlated to returns on risky securities....
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TL;DR: In this article, an optimal unconditional linear performance benchmark is derived to better align incentives within the firm and the authors show that designing appropriate return benchmarks can substantially reduce the costs of decentralized investment management and the value of an optimally designed benchmark.
Abstract: We study an institutional investment problem in which a centralized decision maker, the Chief Investment Officer (CIO), for example, employs multiple asset managers to implement investment strategies in separate asset classes. The CIO allocates capital to the managers who, in turn, allocate these funds to the assets in their asset class. This two-step investment process causes several misalignments of objectives between the CIO and his managers and can lead to large utility costs for the CIO. We focus on (1) loss of diversification, (2) unobservable managerial appetite for risk, and (3) different investment horizons. We derive an optimal unconditional linear performance benchmark and show that this benchmark can be used to better align incentives within the firm. We find that the CIO’s uncertainty about the managers’ risk appetites increases both the costs of decentralized investment management and the value of an optimally designed benchmark. THE INVESTMENT MANAGEMENT DIVISIONS OF BANKS, mutual funds, and pension funds are predominantly structured around asset classes such as equities, fixed income, and alternative investments. To achieve superior returns, either through asset selection or market timing, gathering information about specific assets and capitalizing on the acquired informational advantage requires a high level of specialization. This induces the centralized decision maker of the firm, the Chief Investment Officer (CIO), for example, to pick asset managers who are specialized in a single asset class and to delegate portfolio decisions to these specialists. As a consequence, asset allocation decisions are made in at least two stages. In the first stage, the CIO allocates capital to the different asset classes, each managed by a different asset manager. In the second stage, each manager decides how to allocate the funds made available to him, that is, to the assets within his class. This two-stage process can generate several misalignments of incentives that may lead to large utility costs on the part of the CIO. We show that designing appropriate return benchmarks can substantially reduce these costs.
120 citations
TL;DR: In this article, the authors consider the impact of entrepreneurial risk aversion and incompleteness on investment timing and the value of the option to invest, and find that the option is never exercised (and investment never occurs) in the complete model whereas the entrepreneur exercises the option in the incomplete setting.
Abstract: This paper considers the impact of entrepreneurial risk aversion and incompleteness on investment timing and the value of the option to invest. A risk averse entrepreneur faces the irreversible decision of when to pay a cost in order to receive a one-off investment payoff. The uncertainty associated with the investment payoff can be partly offset by hedging, but the remaining unhedgeable risk is idiosyncratic. Nested within our incomplete set-up is the complete model of McDonald and Siegel (1986) which assumes investment payoffs are perfectly spanned by traded assets. We find risk aversion and idiosyncratic risk erode option value and lower the investment threshold. Our main finding is that there is a parameter region within which the complete and incomplete models give differing investment signals. In this region, the option is never exercised (and investment never occurs) in the complete model, whereas the entrepreneur exercises the option in the incomplete setting. Strikingly, this parameter region corresponds to a negative implicit dividend yield on the payoff, and so this exercise behavior contrasts with conventional wisdom of Merton (1973) for complete markets. Finally, in this parameter region, increased volatility speeds-up investment and option values are not strictly convex in project value, in sharp contrast to the conclusion of standard real options models.
120 citations
TL;DR: In this article, the problem of optimal consumption and portfolio in a jump diffusion market in the presence of proportional transaction costs for an agent with constant relative risk aversion utility was considered and the solution in the jump diffusion case has the same form as in the pure diffusion case first solved by Davis and Norman.
119 citations
References
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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