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, a parsimonious model of the market for immediacy in capital market transactions is developed, which yields an analytically tractable quantity structure of immediacy prices.
Abstract: This paper models transaction costs as the rents that a monopolistic market maker extracts from impatient investors who trade via limit orders. We show that limit orders are American options. The limit prices inducing immediate execution of the order are functionally equivalent to bid and ask prices and can be solved for various transaction sizes to characterize the market maker’s entire supply curve. We find considerable empirical support for the model’s predictions in the cross-section of NYSE firms. The model produces unbiased, out-of-sample forecasts of abnormal returns for firms added to the S&P 500 index. CAPITAL MARKET TRANSACTIONS essentially bundle a primary transaction for the underlying security with a secondary transaction for immediacy. From this perspective, the price of immediacy explains the wedge between transaction prices and fundamental value and therefore represents a cost of transacting. Despite widespread interest among investors and corporations alike, a useful characterization of transaction prices has been elusive. This paper addresses this challenge by developing a parsimonious model of the market for immediacy in capital market transactions that yields an analytically tractable quantity structure of immediacy prices. An inherent friction that limits liquidity in capital markets is the asynchronous arrival of buyers and sellers, each demanding relatively quick transactions. Grossman and Miller (1988) argue that the demand for immediacy in capital markets is both urgent and sustained, creating a role for an intermediary or market maker, who supplies immediacy by standing ready to transact when order imbalances arise (Demsetz (1968)). 1 In this setting, the price of
94 citations
Cites methods from "Optimum consumption and portfolio r..."
...Our model of transaction costs adopts a partial equilibrium framework similar in spirit to the one used for studying individual portfolio choice (Merton (1969, 1971)), in which the process for the asset’s fundamental value is specified exogenously....
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TL;DR: In this paper, the authors show that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies, and the C 2, 1 regularity of the value function is proven.
94 citations
TL;DR: In this paper, the authors examine the intertemporal price cap regulation of a firm that has market power under uncertainty and show that under uncertainty, the monopoly firm will generally under-invest and impose quantity rationing on its customers.
Abstract: This paper examines the intertemporal price cap regulation of a firm that has market power. Under uncertainty, the unconstrained firm ‘waits longer’ before investing or adding to capacity and as a corollary, enjoys higher prices over time than would be observed in an equivalent competitive industry. In the certainty case, the imposition of an inter-temporal price cap can be used to realise the competitive market solution; by contrast, under uncertainty, it cannot. Even if the price cap is optimally chosen, under uncertainty, the monopoly firm will generally (a) under-invest and (b) impose quantity rationing on its customers.
94 citations
TL;DR: In this paper, the authors derived grade selection rules for heterogeneous resource deposits with increasing marginal extraction costs and showed that, contrary to the conventional wisdom, it can be optimal to extract the least-cost deposits last.
94 citations
TL;DR: The results suggest that markets for real estate investment trusts or other house price--linked contracts lead to nonnegligible welfare gains.
Abstract: We derive explicit solutions to life-cycle utility maximization problems involving stock and bond investment, perishable consumption, and the rental and ownership of residential real estate. Prices of houses, stocks and bonds, and labor income are correlated. Because of a positive correlation between house prices and labor income, young individuals want little exposure to house price risk and tend to rent their home. Later in life the desired housing investment increases and will eventually reach and exceed the desired consumption, suggesting that the individual should buy his home---and either additional housing units (for renting out) or house price--linked financial assets. In the final years, preferences shift back to home rental. The derived strategies are still useful if housing positions are only reset infrequently. Our results suggest that markets for real estate investment trusts or other house price--linked contracts lead to nonnegligible welfare gains.
This paper was accepted by Wei Xiong, finance.
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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