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: This article used the theory of real options to solve the problem of education choice in a dynamic stochastic model and showed that education attainment will be an increasing function of the risk associated with education, regardless of the degree of risk aversion.
61 citations
Cites background from "Optimum consumption and portfolio r..."
...For specific examples from financial investment see Merton (1971); for physical capital see Caballero and Engle (1999); for irreversible physical investment (so called “real options”) see Dixit and Pindyck (1994)....
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...…and Rosen (1980) and Altonji (1993) who examine policy effects in stochastic two period models; Keane and Wolpin (1997) who estimated an empirical dynamic model of education choice and Williams (1979) who adapted the portfolio choice model of Merton (1971) to allow for investment in human capital....
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TL;DR: It is shown that the optimal portfolio depends linearly on the supplementary cost of the fund, plus an additional term due to the random evolution of benefits, and the efficient frontier is found.
61 citations
Additional excerpts
...…by n risky assets fSigni¼1, which are correlated geometric Brownian motions, generated by w ¼ ðw1; . . . ;wnÞ >, and a riskless asset S0, as proposed in Merton (1971), that is, whose evolutions are given by the equations: dS0ðtÞ ¼ rS0ðtÞdt; S0ð0Þ ¼ 1; ð2Þ dSiðtÞ ¼ SiðtÞ bi dt þ Xn j¼1 rij dwjðtÞ !...
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TL;DR: The authors empirically analyzes moral hazard in car insurance using a dynamic theory of an insuree's dynamic risk (ex ante moral hazard) and claim (ex post moral hazard), choices and Dutch longitudinal micro data.
Abstract: This paper empirically analyzes moral hazard in car insurance using a dynamic theory of an insuree's dynamic risk (ex ante moral hazard) and claim (ex post moral hazard) choices and Dutch longitudinal micro data We use the theory to characterize the heterogeneous dynamic changes in incentives to avoid claims that are generated by the Dutch experience-rating scheme, and their effects on claim times and sizes under moral hazard We develop tests that exploit these structural implications of moral hazard and experience rating Unlike much of the earlier literature, we find evidence of moral hazard
60 citations
Cites background from "Optimum consumption and portfolio r..."
...…base premium to which the discounts in Table 1 are applied depends on agent i’s characteristics, the mapping Ai will be heterogeneous across agents.15 12For the purpose of our analysis, this is equivalent to assuming that any such income is perfectly foreseen by the agent (Merton, 1971, Section 7)....
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TL;DR: In this article, a review of recent scientific literature on consumer financial decisions over the life cycle, outlining its implications for the design of pension plans, is presented, and the practical implications of the theory of rational financial planning and wealth management are discussed.
60 citations
01 Jun 2011
TL;DR: Return rates and borrowing/lending rate are presented as fuzzy triangular numbers instead of crisp representations to determine the amount of investment in different planning areas especially when the rate of borrowing is greater than that of lending.
Abstract: Investment strategic planning is one of the most important areas of research in financial engineering. The primary concern of this research is to determine the amount of investment in different planning areas especially when the rate of borrowing is greater than that of lending. The proposed research method in this paper is a form of fuzzy linear programming which is capable of determining the amount of investment in different time cycles. In this paper return rates and borrowing/lending rate are presented as fuzzy triangular numbers instead of crisp representations. The developed model can instruct the balance between cash and margin for investors and using fuzzy set theory, their confidence level can be obtained for each produced portfolio. The method is also implemented using some numerical examples and the output results are discussed.
60 citations
Cites background from "Optimum consumption and portfolio r..."
...Selective scope of related topic Reviewed literatures Markowitz seminal model to multi period case Samuelson (1969), Merton (1969, 1971, 1996), Mossin (1968), Zenios et al. (1998), Morey & Morey (1999), Leippold et al. (2004), Briec & Kerstens (2009) Dynamic programming Chryssikou (1998), Hakansson…...
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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