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 management of an aggregated dynamic pension fund is studied and the main finding is that optimal investment policies are of constant proportionality type, and the problem of minimizing the expected discounted cost of reaching a ruin point (resp. beating a desired objective) is solved.
Abstract: In this paper the optimal management of an aggregated dynamic pension fund is studied. To cover the promised liabilities to workers at the age of retirement, the plan sponsor continuously manages time-varying funds. He or she can choose the rate of contribution to the fund, the investment in a given number of risky assets, and a security with constant rate of return. The problem of maximizing the probability that the fund assets achieve some prescribed goal before some undesirable lower value, or ruin point, is first considered. Secondly, the problem of minimizing (resp. maximizing) the expected discounted cost of reaching a ruin point (resp. beating a desired objective) is solved. Finally, maximization of utility function when the fund can suddenly terminate is analyzed. The main finding is that optimal investment policies are of constant proportionality type.
44 citations
Cites background from "Optimum consumption and portfolio r..."
...6 Notice that the stated problem is not exactly the model in Merton (1971), since that utility depends on the controlled process X and not on the control variable as in Merton’s model (the consumption process in that case)....
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...…formed by n risky assets {Si } n i=1, which are correlated geometric Brownian motions generated by w, and a riskless asset S0, as proposed in Merton (1971), that is, whose evolutions are given by the equations: dS0(t) = r S0(t)dt, with r > 0, (3) dSi (t) = Si (t) ( bi dt + n∑ j=1 σi j dw j…...
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TL;DR: The intertemporal portfolio choice approach developed by Merton and the fundamental notion of dynamic hedging are presented and their usefulness for economic insights and numerical implementations is illustrated.
Abstract: This paper reviews portfolio selection models and provides perspective on some open issues. It starts with a review of the classic Markowitz mean-variance framework. It then presents the intertemporal portfolio choice approach developed by Merton and the fundamental notion of dynamic hedging. Martingale methods and resulting portfolio formulas are also reviewed. Their usefulness for economic insights and numerical implementations is illustrated. Areas of future research are outlined.
44 citations
TL;DR: In this article, a model that accounts for empirical macroeconomic regularities accompanying exchange rate crises is presented, assuming the Central Bank can surprise the private sector about its monetary policy, solving for agents' consumption and portfolio decisions and the economy's equilibrium prices and interest rates using an intertemporal asset pricing model.
44 citations
TL;DR: In this paper, the authors investigate the effects of changes in uncertainty about future green goodwill, competitor abatement investments, regulations, etc., using a real options framework, and conclude that increased uncertainty about consumers' willingness to pay for green products in the future discourage voluntary abatements investments.
Abstract: In this paper we adopt the green goodwill argument as to why firms voluntarily invest in abatement capital. We investigate the effects on the abatement investment decision of changes in uncertainty about future green goodwill, competitor abatement investments, regulations, etc., using a real options framework. Our results indicate that increased uncertainty about consumers' willingness to pay for “green” products in the future discourage voluntary abatement investments. The model also suggests that voluntary abatement investments are promoted by an increased threat of regulation and competitor abatement investments. Furthermore, the benefit-cost ratio of the abatement investment project, at the point where it is optimal to invest, is independent of what regulatory regime (stringent or lenient) the firm operates in. We also conclude that despite the fact that voluntary abatement investment exists, there may still be room for environmental policy.
44 citations
TL;DR: In this paper, a dynamic portfolio choice framework is proposed to evaluate the effect of managers' risk exposure on the performance of a mutual fund, and the authors demonstrate how a simple risk management practice that accounts for benchmarking can ameliorate the adverse effects of managerial incentives.
Abstract: Money managers are rewarded for increasing the value of assets under management, and predominantly so in the mutual fund industry. This gives the manager an implicit incentive to exploit the well-documented positive fund-flows to relative-performance relationship by manipulating her risk exposure. In a dynamic portfolio choice framework, we show that as the year-end approaches, the ensuing convexities in the manager's objective induce her to closely mimic the index, relative to which her performance is evaluated, when the fund's year-to-date return is sufficiently high. As her relative performance falls behind, she chooses to deviate from the index by either increasing or decreasing the volatility of her portfolio. The maximum deviation is achieved at a critical level of underperformance. It may be optimal for the manager to reach such deviation via selling the risky asset despite its positive risk premium. Under multiple sources of risk, with both systematic and idiosyncratic risks present, we show that optimal managerial risk shifting may not necessarily involve taking on any idiosyncratic risk. Costs of misaligned incentives to investors resulting from the manager's policy are economically significant. We then demonstrate how a simple risk management practice that accounts for benchmarking can ameliorate the adverse effects of managerial incentives.
44 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