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: The authors used preference-free dominance arguments to develop a framework for locating the optimal age at which a retiree should purchase an irreversible life annuity, as a function of current annuity prices and mortality tables.
Abstract: We use preference-free dominance arguments to develop a framework for locating the optimal age (time) at which a retiree should purchase an irreversible life annuity, as a function of current annuity prices and mortality tables. Then, using the institutional characteristics of annuity markets in the US, we show that annuitization prior to age 65–70 is dominated by self-annuitization even in the absence of any bequest motives. And, for retirees who are willing to accept some financial risk in exchange for retaining the benefits of liquidity and bequest, the optimal age can be even later. In addition to the normative implications, these results should help shed light on the so-called annuity puzzle which has been much debated by economists, by focusing attention on the specific ages for which a puzzle can actually be said to exist.
50 citations
TL;DR: In this paper, options on certain agricultural futures are being traded in the United States under a three-year pilot program administered by the Commodity Futures Trading Commission (CFTC).
Abstract: The pricing of options on futures has generated much recent interest from both an academic as well as a trading persp ctive. These conti gent claims provide new avenues for the allocation of price risk among investors and have been well received by the financial markets. For example, options on Treasury bond futures began trading at the Chicago Board of Trade in 1982 and have been a very successful innovation. This success has assured the commodity exchanges of the value of options trading, and the development of options on other types of futures is being accelerated. Currently, options on certain agricultural futures are being traded in the United States under a three-year pilot program administered by the Commodity Futures Trading Commission. Many recent academic studies have made significant contributions to option pricing theory using varying asset price behavior assumptions. Among these are the Black-Scholes formula (1973), Roll's American call option formula (1977), Cox's constant elasticity of variance (CEV) formula (1975), Merton's jump-diffusion formula (1976), Binomial pricing method (Cox, Ross, and Rubinstein, ) 979), and various numerical methods for option pricing. Each of the above formulas and methods is based on the continuous-time (or limiting case)! no-arbitrage pricing framework of Black and Scholes. Within this
50 citations
TL;DR: This paper investigates an optimal investment problem faced by a defined contribution (DC) pension fund manager under inflationary risk and presents a way to deal with the optimization problem, in case there is a (positive) endowment (or contribution), using the martingale method.
Abstract: This paper investigates an optimal investment problem faced by a defined contribution (DC) pension fund manager under infationary risk. It is assumed that a representative member of a DC pension plan contributes a fixed share of his salary to the pension fund during time horizon [0,T]. The pension contributions are invested continuously in a risk-free bond, an index bond and a stock. The objective is to maximize the expected utility of terminal value of the pension fund. By solving this investment problem we present a way of how to deal with the optimization problem, in the case there is a (positive) endowment (or contribution), using the Martingale method.
50 citations
Cites background or methods from "Optimum consumption and portfolio r..."
...Bodie et al. (1992) derive analytic solutions for a problem of this type, but the setup is quite specific and does not apply to our case....
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...With regards to the set of admissible portfolios, we first follow the classical line taken in Merton (1971) , Karatzas (1997) and Koo (1995), which allowed the agent to borrow against expected future income....
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...In terms of Bodie et al. (1992) V (t) corresponds to the total wealth process, comprising financial wealth and a share of human capital....
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...These are the dynamic programming approach (see Merton (1969, 1971) ) and the Martingale method (see Karatzas et al. 1986; Pliska 1986; Cox/Huang 1989)....
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...H (s) H (t) cY(s)ds � is what Bodie et al. (1992) call human capital, 2 or more precisely a share c of it. This setup therefore takes into account the fact, that agents do not only base their investment decisions on their current financial wealth, but also on their individual human capitals....
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TL;DR: In this paper, a simple yet completely general model for foreign exchange rates (FXR) in the context of multidimensional, possibly incomplete, Ito SDE market/econometric models is presented.
Abstract: We establish a simple, yet completely general model for foreign exchange rates (FXR), in the context of multidimensional, possibly incomplete, Ito SDE market/econometric models. A very simple example is presented as well.
49 citations
TL;DR: In this paper, a risk-averse entrepreneur with access to a profitable venture needs to raise funds from investors and cannot indefinitely commit her human capital to the venture, which limits the firm's debt capacity, distorts investment and compensation, and constrains the entrepreneur's risk sharing.
Abstract: A risk‐averse entrepreneur with access to a profitable venture needs to raise funds from investors. She cannot indefinitely commit her human capital to the venture, which limits the firm's debt capacity, distorts investment and compensation, and constrains the entrepreneur's risk sharing. This puts dynamic liquidity and state‐contingent risk allocation at the center of corporate financial management. The firm balances mean‐variance investment efficiency and the preservation of financial slack. We show that in general the entrepreneur's net worth is overexposed to idiosyncratic risk and underexposed to systematic risk. These distortions are greater the closer the firm is to exhausting its debt capacity.
49 citations
Cites methods from "Optimum consumption and portfolio r..."
...The firm’s investment policy then approaches the Hayashi (1982) risk-adjusted first-best benchmark, and its consumption and asset allocations approach the generalized Merton (1971) consumption and mean-variance portfolio rules....
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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